Form 424B5 OnKure Therapeutics,

Filed pursuant to Rule 424(b)(5)
Registration Statement No. 333-291334

PROSPECTUS SUPPLEMENT

(To Prospectus Supplement dated November 26, 2025

and Prospectus dated November 26, 2025)

Up to $100,000,000

Class A Common Stock

This prospectus supplement amends and supplements the information in the prospectus supplement dated November 26, 2025 (the “ATM Prospectus Supplement”) and the accompanying prospectus, dated November 26, 2025 (together with the ATM Prospectus Supplement, the “Prospectus”), filed with the Securities and Exchange Commission as a part of our registration statement on Form S-3 (File No. 333-291334) on November 6, 2025, relating to the offer and sale of shares of our Class A common stock, par value $0.0001 per share (“Class A Common Stock”), pursuant to that certain sales agreement, dated November 6, 2025 (the “Sales Agreement”), by and between us and Leerink Partners LLC (“Leerink Partners”).

We are filing this prospectus supplement to amend the Prospectus because we are no longer subject to General Instruction I.B.6. of Form S-3, which limits the amounts that we may sell under the registration statement of which this prospectus supplement and the Prospectus are a part. If we become subject to the offering limits of General Instruction I.B.6 in the future, we will file another prospectus supplement. As of August 4, 2026, we have not yet offered or sold any shares of Class A Common Stock under the Prospectus.

This prospectus supplement should be read in conjunction with the Prospectus, and is qualified by reference thereto, except to the extent that the information herein amends or supersedes the information contained in the Prospectus. This prospectus supplement is not complete without, and may only be delivered or utilized in connection with, the Prospectus and any future amendments or supplements thereto.

Our Class A Common Stock is listed on the Nasdaq Global Market under the symbol “OKUR.” The aggregate market value of our outstanding Class A Common Stock held by non-affiliates as of August 3, 2026 pursuant to General Instruction I.B.6 of Form S-3 is $167.3 million, which was calculated based on 36,368,892 shares of our Class A Common Stock outstanding held by non-affiliates and at a price of $4.60 per share, the closing price of our Class A Common Stock on July 6, 2026. In accordance with the terms of the Sales Agreement, we are registering the offer and sale of shares of our Class A Common Stock having an aggregate offering price up to $100,000,000 from time to time through or to Leerink Partners acting as our agent or principal. The compensation to Leerink Partners for sales of Class A Common Stock sold pursuant to the Sales Agreement will be an amount up to 3.0% of the gross proceeds of the sales price per share of Class A Common Stock sold under the Sales Agreement.

We are an “emerging growth company” and “smaller reporting company,” each as defined under the federal securities laws, and as such, are subject to certain reduced public company reporting requirements. See “Prospectus Supplement Summary—Implications of Being an Emerging Growth Company” and “Prospectus Supplement Summary—Implications of Being a Smaller Reporting Company” on page S-2 of the Prospectus.

Investing in our securities involves risks. Please carefully read the information under the headings “Risk Factors” beginning on page S-6 of the Prospectus and “Item 1A – Risk Factors” of our most recent report on Form 10-K or 10-Q that is incorporated by reference in this prospectus supplement before you invest in our securities.

Neither the Securities and Exchange Commission nor any state securities commission has approved or disapproved of these securities or passed upon the adequacy or accuracy of this prospectus supplement. Any representation to the contrary is a criminal offense.

Leerink Partners

The date of this prospectus supplement is August 4, 2026.