UNITED STATES SECURITIES AND EXCHANGE COMMISSION

Washington, D.C. 20549

FORM 6-K

REPORT OF FOREIGN PRIVATE ISSUER PURSUANT TO RULE 13A-16 OR 15D-16 UNDER THE SECURITIES EXCHANGE ACT OF 1934

For the month of June 2026

Commission File Number: 001-42684

RUBICO INC.

(Translation of registrant’s name into English)

20 Iouliou Kaisara Str
19002 Paiania

Athens, Greece

(Address of principal executive office)

Indicate by check mark whether the registrant files or will file annual reports under cover of Form 20-F or Form 40-F:

Form 20-F ☒ Form 40-F ☐

INFORMATION CONTAINED IN THIS FORM 6-K REPORT

Warrant Inducement Agreement

On June 12, 2026, Rubico Inc. (“we” or the “Company”), entered into a warrant exercise inducement letter agreement (“Inducement Letter”) with the existing holders of all of the Company’s outstanding Class C warrants issued on May 21, 2026 (the “Class C Warrants”), exercisable to purchase up to an aggregate of 7,894,740 of the Company’s common shares, par value $0.01 (the “Common Shares”), pursuant to which the holders agreed to exercise all of the outstanding Class C Warrants at an exercise price reduced from $0.95 per share to $0.65 per share. The net proceeds of the exercise of the Class C Warrants to the Company, after deducting estimated expenses and fees, are expected to be approximately $4.8 million. In connection with the transaction described above, the Company entered into a financial advisory services agreement, dated June 12, 2026, with Maxim Group LLC (“Maxim”), pursuant to which the Company has agreed to pay Maxim for its services a cash fee of up to 6% of the gross proceeds received by the Company in connection with the exercise of the Existing Warrants.

The issuance of the Common Shares underlying the Class C Warrants was registered pursuant to the Company’s registration statement on Form F-1 (File No. 333-295716), filed with the Securities and Exchange Commission (the “Commission”), which became effective with the Commission on May 20, 2026.

In consideration for the immediate exercise of the Class C Warrants for cash, the exercising holders will receive new warrants to purchase up to an aggregate of 15,789,480 Common Shares (the “Class D Warrants”) in a private placement pursuant to Section 4(a)(2) of the Securities Act of 1933, as amended (the “Securities Act”). The Class D Warrants will be issued within 15 days following the date of the Inducement Letter and are immediately exercisable upon issuance at an exercise price of $0.65 per Common Share and will expire five years after issuance. The form of Class D Warrant is filed as an exhibit to this report and is incorporated herein by reference.

The Class D Warrants described above were offered in a private placement pursuant to an applicable exemption from the registration requirements of the Securities Act and, along with the common shares issuable upon their exercise, have not been registered under the Securities Act, and may not be offered or sold in the United States absent registration with the SEC or an applicable exemption from such registration requirements. The securities were offered only to accredited investors. The Company has agreed to file a registration statement with the SEC covering the resale of common shares issuable upon exercise of the Class D Warrants.

This report shall not constitute an offer to sell or a solicitation of an offer to buy these securities, nor shall there be any sale of these securities in any state or jurisdiction in which such an offer, solicitation or sale would be unlawful prior to registration or qualification under the securities laws of any such state or jurisdiction.

Class D Warrants

The following summary of certain terms and provisions of the Class D Warrants is not complete and is subject to, and qualified in its entirety by, the provisions of the form of Class D Warrant furnished as an exhibit to this report.

Exercisability. The Class D Warrants are immediately exercisable at any time after their issuance and at any time up to the date that is five years after their issuance. Each of the Class D Warrants will be exercisable, at the option of each holder, in whole or in part by delivering to us a duly executed exercise notice with payment in full in immediately available funds for the number of Common Shares purchased upon such exercise (except in the case of a cashless exercise, as discussed below). We may be required to pay certain amounts as liquidated damages as specified in the Class D Warrants in the event we do not deliver Common Shares upon exercise of the Class D Warrants within the time periods specified in the Class D Warrants. No fractional Common Shares will be issued in connection with the exercise of a Class D Warrant.

Cashless Exercise. If a registration statement registering the issuance of the Common Shares underlying the Class D Warrants under the Securities Act of 1933, as amended (the “Securities Act”) is not effective or available, the holder may, in its sole discretion, elect to exercise the Class D Warrant through a cashless exercise, in which case the holder would receive upon such exercise the net number of Common Shares determined according to the formula set forth in the Class D Warrant.

Exercise Limitation. A holder will not have the right to exercise any portion of the Class D Warrants if the holder (together with its affiliates) would beneficially own in excess of 4.99% (or, upon election of the holder prior to the issuance of any warrants, up to 9.99%) of the number of our Common Shares outstanding immediately after giving effect to the exercise, as such percentage ownership is determined in accordance with the terms of the warrants. However, any holder may increase or decrease such percentage to any other percentage not in excess of 9.99%, upon at least 61 days’ prior notice from the holder to us with respect to any increase in such percentage.

Exercise Price. The exercise price per whole Common Share purchasable upon exercise of the Class D Warrants is $0.65 per share. The exercise price of the Class D Warrants may also be reduced to any amount and for any period of time at the sole discretion of the Board of Directors. The exercise price and number of Common Shares issuable on exercise are subject to appropriate adjustments in the event of certain dividends and distributions, stock splits, stock combinations, reclassifications or similar events affecting our Common Shares.

Transferability. Subject to applicable laws, the Class D Warrants may be offered for sale, sold, transferred or assigned without our consent.

Exchange Listing. We do not intend to list the Class D Warrants on any securities exchange or other trading market. Without an active trading market, the liquidity of the Class D Warrants will be limited.

Rights as a Shareholder. Except as otherwise provided in the Class D Warrants or by virtue of such holder’s ownership of our Common Shares, the holder of a Class D Warrant does not have the rights or privileges of a holder of our Common Shares, including any voting rights, until the issuance of Common Shares upon exercise of the Class D Warrant. Holders of Class D Warrants have the right to participate in certain distributions as specified in the Class D Warrant.

Fundamental Transactions. In the event of a fundamental transaction, as described in the Class D Warrants and generally including, with certain exceptions, any reorganization, recapitalization or reclassification of our Common Shares, the sale, transfer or other disposition of all or substantially all of our properties or assets, our consolidation or merger with or into another person, the acquisition of more than 50% of our outstanding Common Shares or 50% of the voting power represented by our outstanding Common Shares, the holders of the Class D Warrants will be entitled to receive upon exercise of the Class D Warrants the kind and amount of securities, cash or other property that the holders would have received had they exercised the Class D Warrants immediately prior to such fundamental transaction. In addition, in the event of a fundamental transaction, we or the successor entity, at the request of a holder of Class D Warrants, will be obligated to purchase any unexercised portion of such Class D Warrants in accordance with the terms of the Class D Warrants.

Governing Law. The Class D Warrants are governed by New York law.

Supplemental Risk Factors

The risk factors set forth below supplement and should be read together with those risk factors set forth under the heading “Risk Factors” in our Annual Report on Form 20-F, filed with the Commission on March 23, 2026.

We have in the past and may in the future rely in part on equity issuances, which will not require shareholder approval, to fund our growth, and such equity issuances could dilute your ownership interests and may depress the market price of our Common Shares.

We may issue additional Common Shares or other equity securities of equal or senior rank in the future in connection with, among other things, future vessel acquisitions or repayment of outstanding indebtedness, without shareholder approval, in a number of circumstances.

As part of our business strategy, we have in the past and may in the future rely in part on issuances of equity, warrants or preferred securities, which may carry voting rights and may be convertible or exercisable into Common Shares, to fund the growth of our fleet. We may issue such securities in private placements, including to related parties, or in registered offerings.

Under a common shares purchase agreement entered into with B. Riley Principal Capital II, LLC (the “Selling Shareholder”) on July 21, 2025, we have the right to sell to the Selling Shareholder from time to time up to $30,000,000 of our Common Shares, of which we have sold $22.9 million to date, and under a common shares purchase agreement (together with the July 21, 2025 agreement with the Selling Shareholder, the “Equity Line Purchase Agreements”) entered into with the Selling Shareholder, we have the right to sell to the Selling Shareholder from time to time up to an additional $50,000,000 of our Common Shares, in each case subject to certain limitations and conditions set forth in the Equity Line Purchase Agreements. We have registered under the Securities Act the resale by the Selling Shareholder of Common Shares sold under the Equity Line Purchase Agreements.

Further, as contemplated by a share purchase agreement to purchase a newbuilding mega yacht, Top Ships Inc. may, under certain circumstances, demand the payment of installments in the form of Series E Preferred Shares. The Series E Preferred Shares would, if issued, be convertible into Common Shares. As of the date of this prospectus, there are no Series E Preferred Shares. For a description of the Series E Preferred Shares, see our Current Report on Form 6-K filed on January 2, 2026.

Further, as contemplated by a share purchase agreement to purchase all of the issued and outstanding shares of Roman Shark IX Inc., a company that has entered into a shipbuilding contract for a 47,499 dwt chemical/product oil carrier, we have issued to Central Mare Inc. 4,236 Series G Perpetual Convertible Preferred Shares (the “Series G Preferred Shares”). The Series G Preferred Shares are convertible, at our option, into Common Shares. As of the date hereof and giving effect to the Inducement Letter, the Series G Preferred Shares have a conversion price of $0.6 and are convertible into 7,060,000 common shares, as may be further adjusted. For a description of the Series G Preferred Shares, see our Current Report on Form 6-K filed on February 23, 2026.

As of the date hereof and giving effect to the transactions contemplated by the Inducement Letter, we expect there will be 15,670,898 Common Shares outstanding. In addition, there are 395,635 Common Shares issuable under our outstanding January Placement Agent Warrants, Class B Warrants and May Placement Agent Warrants.

Our issuance of additional Common Shares, including pursuant to the Equity Line Purchase Agreements, or otherwise upon conversion of convertible securities or exercise of warrants, or other equity securities of equal or senior rank, or with voting rights, may have the following effects:

Our existing common shareholders’ proportionate ownership interest in us will decrease and they may suffer economic dilution of their interest in us;

the amount of cash available for dividends payable per Common Share may decrease;

the relative voting strength of each previously outstanding Common Share may be diminished; and

the market price of our Common Shares may decline.

The market price of our Common Shares has been and may in the future be subject to significant fluctuations.

The market price of our Common Shares has been and may in the future be subject to significant fluctuations as a result of many factors, some of which are beyond our control.

Among the factors that could in the future affect our stock price are:

variations in our results of operations;

changes in market valuations of similar companies and stock market price and volume fluctuations generally;

changes in earnings estimates or the publication of research reports by analysts;

speculation in the press or investment community about our business or the shipping industry generally;

strategic actions by us or our competitors such as acquisitions or restructurings;

the thin trading market for our Common Shares, which makes it somewhat illiquid;

regulatory developments;

additions or departures of key personnel;

general market conditions; and

domestic and international economic, market and currency factors unrelated to our performance.

The stock markets in general, and the markets for shipping and shipping stocks in particular, have experienced extreme volatility that has sometimes been unrelated to the operating performance of individual companies. These broad market fluctuations may adversely affect the trading price of our Common Shares.

We have experienced and may in the future experience rapid and substantial share price volatility unrelated to our actual or expected operating performance, financial condition or prospects, making it difficult for prospective investors to assess the rapidly changing value of our Common Shares.

As a relatively small-capitalization company with relatively small public float, we may experience greater share price volatility, extreme price run-ups or rapid price declines, larger spreads in bid and ask prices, lower trading volume and less liquidity than large-capitalization companies. Such volatility, including any share price run-up, may be unrelated to our actual or expected operating performance, financial condition or prospects, making it difficult for prospective investors to assess the rapidly changing value of our Common Shares. In addition, holders of our Common Shares may experience losses, which may be material, if the price of our Common Shares declines after the Offering or if such investors purchase our Common Shares prior to any price decline.

For example, on June 11, 2026, the trading price of our Common Shares ranged from an intra-day high of $1.07 to an intra-day low of $0.48 on trading volume of approximately 165.3 million shares.

Furthermore, if the trading volumes of our Common Shares are low, investors buying or selling in relatively small quantities may be able to easily influence the price of our Common Shares. Such low volume of trades could also cause the price of our Common Shares to fluctuate greatly, with large percentage changes in share price occurring in any trading day session. Holders of our Common Shares may also not be able to readily liquidate their investment or may be forced to sell at depressed prices due to low volume trading. Broad market fluctuations and general economic and political conditions may also adversely affect the market price of our Common Shares. As a result of this volatility, investors may experience losses on their investment in our Common Shares. A decline in the market price of our Common Shares also could adversely affect our ability to issue additional Common Shares or other securities and our ability to obtain additional financing in the future. Also see “-The market price of our Common Shares has been and may in the future be subject to significant fluctuations” above.

A possible “short squeeze” due to a sudden increase in demand of our Common Shares that largely exceeds supply may lead to further price volatility in our Common Shares.

Investors may purchase our Common Shares to hedge existing exposure in our Common Shares or to speculate on the price of our Common Shares. Speculation on the price of our Common Shares may involve long and short exposures. To the extent aggregate short exposure exceeds the number of Common Shares available for purchase in the open market, investors with short exposure may have to pay a premium to repurchase our Common Shares for delivery to lenders of our Common Shares. Those repurchases may in turn, dramatically increase the price of our Common Shares until investors with short exposure are able to purchase additional Common Shares to cover their short position. This is often referred to as a “short squeeze.” Following such a short squeeze, once investors purchase the shares necessary to cover their short position, the price of our Common Shares may rapidly decline. A short squeeze could lead to volatile price movements in our Common Shares that are not directly correlated to the performance or prospects of our company.

Cautionary Note Regarding Forward-Looking Statements

Matters discussed in this Report may constitute forward-looking statements. The Private Securities Litigation Reform Act of 1995 provides safe harbor protections for forward-looking statements in order to encourage companies to provide prospective information about their business. Forward-looking statements include statements concerning plans, objectives, goals, strategies, future events or performance, and underlying assumptions and other statements, which are other than statements of historical facts.

The Company desires to take advantage of the safe harbor provisions of the Private Securities Litigation Reform Act of 1995 and is including this cautionary statement in connection with this safe harbor legislation. The words “believe,” “anticipate,” “intends,” “estimate,” “forecast,” “project,” “plan,” “potential,” “may,” “should,” “expect,” “pending,” and similar expressions identify forward-looking statements.

The forward-looking statements in this report are based upon various assumptions, many of which are based, in turn, upon further assumptions, including, without limitation, management's examination of historical operating trends, data contained in the Company’s records, and other data available from third parties. Although the Company believes that these assumptions were reasonable when made, because these assumptions are inherently subject to significant uncertainties and contingencies which are difficult or impossible to predict and are beyond the Company’s control, the Company cannot assure you that it will achieve or accomplish these expectations, beliefs, or projections.

In addition to these assumptions, important factors that, in the Company’s view, could cause actual results to differ materially from those discussed in the forward-looking statements include, among other things:

the Company’s ability to maintain or develop new and existing customer relationships with major crude oil companies and major commodity traders, including its ability to enter into long-term charters for its vessels and those it may acquire in the future;

the Company’s future operating and financial results;

the Company’s future vessel acquisitions, its business strategy and expected and unexpected capital spending or operating expenses, including any dry-docking, crewing, bunker costs and insurance costs;

the Company’s financial condition and liquidity, including its ability to pay amounts that it owes and to obtain financing in the future to fund capital expenditures, acquisitions and other general corporate activities;

oil tanker industry trends, including fluctuations in charter rates and vessel values and factors affecting vessel supply and demand;

the Company’s ability to take delivery of, integrate into its fleet, and employ any newbuildings it may acquire or order in the future and the ability of shipyards to deliver vessels on a timely basis;

the Company’s dependence on its fleet manager to operate its business;

the aging of the Company’s vessels, and those it may acquire in the future, and resultant increases in operation and dry-docking costs;

the ability of the Company’s vessels, and any vessels it may acquire in the future, to pass classification inspections and vetting inspections by oil majors;

significant changes in vessel performance, including increased vessel breakdowns;

the creditworthiness of the Company’s charterers and the ability of its contract counterparties to fulfill their obligations to the Company;

the Company’s ability to repay outstanding indebtedness, to obtain additional financing and to obtain replacement charters for its vessels, and any vessels it may acquire in the future, in each case, at commercially acceptable rates or at all;

changes to governmental rules and regulations or actions taken by regulatory authorities and the expected costs thereof;

the Company’s ability to maintain the listing of its Common Shares on The Nasdaq Stock Market LLC or another trading market, in particular, after the Offering;

the Company’s ability to comply with additional costs and risks related to its environmental, social and governance policies;

potential liability from litigation and the Company’s vessel operations, including purported discharge of pollutants;

changes in general economic and business conditions;

general domestic and international political conditions, potential disruption of shipping routes due to accidents, political events, including “trade wars,” piracy, acts by terrorists or other hostilities or conflicts, including the war between the United States, Israel and Iran, the war in Ukraine, the war between Israel and Hamas, the Houthi crisis in and around the Red Sea, current instability in Venezuela and Iran and potential tensions between the U.S. and Greenland, Denmark or Venezuela;

changes in production of or demand for oil, either globally or in particular regions;

the strength of world economies and currencies, including fluctuations in charterhire rates and vessel values;

potential liability from future litigation and potential costs due to the Company’s vessel operations, and the operation of any vessels it may acquire in the future, including due to any environmental damage and vessel collisions;

the length and severity of public health threats, epidemics and pandemics and other disease outbreaks and their impact on the demand for commercial seaborne transportation and the condition of the financial markets and governmental responses thereto; and

other important factors discussed in “Item 3. Key Information-D. Risk Factors” of the Company’s Annual Report on Form 20-F, filed with the Commission on March 23, 2026 or described from time to time in the reports filed by the Company with the Commission.

Should one or more of the foregoing risks or uncertainties materialize, or should any of the Company’s assumptions prove incorrect, actual results may vary in material respects from those projected in these forward-looking statements. Consequently, there can be no assurance that actual results or developments anticipated by the Company will be realized or, even if substantially realized, that they will have the expected consequences to, or effects, on it. Given these uncertainties, you are cautioned not to place undue reliance on such forward-looking statements.

The Company undertakes no obligation to update or revise any forward-looking statements, whether as a result of new information, future events or otherwise, except as may be required under applicable laws. If one or more forward-looking statements are updated, no inference should be drawn that additional updates will be made with respect to those or other forward-looking statements.

Exhibit Index

Exhibit No.	Description
4.1	Form of Class D Warrant
10.1	Form of Warrant Inducement Agreement

SIGNATURES

Pursuant to the requirements of the Securities Exchange Act of 1934, as amended, the registrant has duly caused this report to be signed on its behalf by the undersigned hereunto duly authorized.

	Rubico Inc. (Registrant)

Date: June 12, 2026	By: /s/ Nikolaos Papastratis
	Nikolaos Papastratis
	Chief Financial Officer

Rubico Inc. 6-K