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

OF THE SECURITIES EXCHANGE ACT OF 1934

July 2026

Commission File Number: 001-43208

The Metals Royalty Company Inc.

1900 Dome Tower

333 7^th Ave SW

Calgary, AB, T2P 2Z1

British Columbia, Canada

(403) 984-1941

(Address of principal executive offices)

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

Form 20-F x          Form 40-F ¨

INFORMATION CONTAINED IN THIS FORM 6-K REPORT

Extension of Closing Date for Additional Mesabi Royalty

On July 31, 2026, The Metals Royalty Company Inc. (“TMCR” or the “Company”) agreed with Mesabi Metallics Company LLC (“Mesabi Metallics”) and Essar to extend the closing under the royalty purchase agreement, as amended (the “Royalty Purchase Agreement”), relating to the Company’s previously announced option to acquire an additional 1.0% Index-Priced Gross Overriding Production Royalty with a Revenue Floor (the “Additional Mesabi Royalty”) in the Mesabi Metallics iron ore project in Nashwauk, Minnesota (the “Mesabi Project”), to August 15, 2026, with an option for TMCR to further extend to August 21, 2026. The Company intends to close the acquisition of the Additional Mesabi Royalty on the same economic terms as its initial 1.0% Mesabi Royalty acquisition, which closed on May 31, 2026.

Upon closing, the Additional Mesabi Royalty would double TMCR’s total royalty interest in the Mesabi Project to 2.0%, bringing anticipated annual royalty cash flow to approximately $22 million per annum at 7.28 Mtpa over a 23-year mine life, with a near-term pathway to 8.5 Mtpa and approximately $26 million per annum. At the project level, based on Mesabi Metallics’ latest report, engineering and procurement continue to near full completion, the Concentrator Control Room has been commissioned and is now operational, and the Primary Crusher Building has completed its start-up trial run – keeping the project on track for full commissioning in Q3 and first production in Q4 2026.

No Offer or Solicitation

This Report on Form 6-K is for informational purposes only and does not constitute an offer to sell, or the solicitation of an offer to buy, any securities of the Company, nor shall there be any sale of securities in any jurisdiction in which such offer, solicitation or sale would be unlawful. Any offering of securities will be made only by means of a prospectus meeting the requirements of Section 10 of the Securities Act of 1933, as amended (the “Securities Act”), or pursuant to an available exemption from the registration requirements thereof.

Cautionary Note Regarding Forward-Looking Statements

The Private Securities Litigation Reform Act of 1995 provides a safe harbor for forward-looking statements made by us or on our behalf. This Report on Form 6-K contains “forward-looking statements” within the meaning of Section 27A of the Securities Act and Section 21E of the Securities Exchange Act of 1934, as amended, and “forward-looking information” within the meaning of applicable securities laws, which reflect the expectations of the Company’s management regarding its future growth, future business plans and opportunities, expected activities and other statements about future events, results or performance. These forward-looking statements include, among other things, statements relating to the extension of the closing deadline; the anticipated timing of, and the Company’s ability to complete, the acquisition of the Additional Mesabi Royalty; the Company’s ability to obtain financing and the terms of any such financing; the estimated royalty revenue and production rates set forth above and the assumptions underlying those estimates; the construction, commissioning, ramp-up, mine life and economic potential of the Mesabi Project; the potential impact of government policy; market opportunity; and the Company’s ability to execute on its business plan and to acquire and manage additional royalty interests. When the Company or its management uses words such as “may,” “will,” “intend,” “should,” “believe,” “expect,” “anticipate,” “project,” “estimate,” “target,” “potential,” “pathway” or similar expressions that do not relate solely to historical matters, it is making forward-looking statements. Forward-looking statements are not guarantees of future performance and are based on a number of estimates and assumptions of management, in light of management’s experience and perception of trends, current conditions and expected developments, as well as other factors that management believes to be relevant and reasonable in the circumstances as of the date of this Report on Form 6-K. Forward-looking statements involve risks and uncertainties that may cause actual results to differ materially from those expressed or implied in such statements. These risks and uncertainties include, but are not limited to: the Company’s inability to obtain financing on acceptable terms or at all, and the dilutive effect of any financing the Company may obtain; the failure to complete the acquisition of the Additional Mesabi Royalty by the extended deadline or at all, and the consequences of any such failure; the risk that the closing deadline is not further extended; the ability of Mesabi Metallics to complete construction of, commission and ramp up the Mesabi Project on the anticipated timeline or at all; the Company’s dependence on the performance of, and information provided by, the operators of the projects underlying the Company’s royalty interests; volatility in iron ore prices and the index-pricing and revenue floor mechanics of the Company’s royalties; the timing and amount of any royalty revenue under the Company’s royalties; the Company’s limited operating history and the risks associated with new business development; the Company’s potential inability to acquire additional royalty, stream or similar interests, or to achieve profitability and positive cash flow; market conditions; competitive dynamics; regulatory changes; and the other factors discussed in the “Risk Factors” section of the Company’s Annual Report on Form 20-F and its subsequent reports furnished to or filed with the U.S. Securities and Exchange Commission, which are available at www.sec.gov. For these reasons, among others, investors are cautioned not to place undue reliance upon any forward-looking statements in this Report on Form 6-K. Any forward-looking statement speaks only as of the date of this Report on Form 6-K, and the Company undertakes no obligation to update or revise any forward-looking statement, whether as a result of new information, future events or otherwise, except as required by applicable law.

SIGNATURE

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

Date: July 31, 2026