SEC Form 424B3 filed by OnKure Therapeutics Inc.

2,938,005 Shares of Class A Common Stock

This prospectus supplement updates and amends the prospectus dated March 21, 2025 (as supplemented to date, the “Prospectus”), which forms a part of our Registration Statement on Form S-1 (Registration Statement No. 333-282792) for which Post-Effective Amendment No.1 was filed with the Securities and Exchange Commission (the “SEC”) on March 20, 2025 and declared effective by the SEC on March 21, 2025.

The Prospectus and this prospectus supplement relate to the resale by certain of the selling securityholders named in the Prospectus (each a “selling securityholder” and, collectively, the “selling securityholders”) of 2,938,005 shares of Class A Common Stock, par value $0.0001 per share (the “Common Stock”) issued in the PIPE Financing (as defined in the Prospectus). The Prospectus also covers any additional securities that may become issuable by reason of stock splits, stock dividends or other similar transactions.

This prospectus supplement should be read in conjunction with the Prospectus, which is to be delivered with this prospectus supplement. This prospectus supplement updates, amends and supplements the information included or incorporated by reference in the Prospectus. If there is any inconsistency between the information in the Prospectus and this prospectus supplement, you should rely on the information in this prospectus supplement.

This prospectus supplement is not complete without, and may not be delivered or utilized except in connection with, the Prospectus, including any amendments or supplements to it.

Current Report on Form 8-K

On May 28, 2025, we filed a Current Report on Form 8-K with the SEC. The Current Report is attached hereto.

We are an “emerging growth company,” as defined under the federal securities laws, and, as such, may elect to comply with certain reduced public company reporting requirements for future filings.

Investing in our securities involves a high degree of risk. Before buying any securities, you should carefully read the discussion of the risks of investing in our securities in the section titled “Risk Factors” beginning on page 9 of the Prospectus.

You should rely only on the information contained in the Prospectus, this prospectus supplement, or any further prospectus supplement or amendment hereto. We have not authorized anyone to provide you with different information.

Neither the Securities and Exchange Commission nor any state securities commission has approved or disapproved of these securities or determined if this prospectus is truthful or complete. Any representation to the contrary is a criminal offense.

The date of this prospectus supplement is May 28, 2025.

UNITED STATES
SECURITIES AND EXCHANGE COMMISSION
WASHINGTON, D.C. 20549

FORM 8-K

CURRENT REPORT

Pursuant to Section 13 or 15(d) of the Securities Exchange Act of 1934

OnKure Therapeutics, Inc.

(Exact name of Registrant as Specified in Its Charter)

(Former Name or Former Address, if Changed Since Last Report)

Check the appropriate box below if the Form 8-K filing is intended to simultaneously satisfy the filing obligation of the registrant under any of the following provisions:

Securities registered pursuant to Section 12(b) of the Act:

Indicate by check mark whether the registrant is an emerging growth company as defined in Rule 405 of the Securities Act of 1933 (§ 230.405 of this chapter) or Rule 12b-2 of the Securities Exchange Act of 1934 (§ 240.12b-2 of this chapter).

Emerging growth company ☒

If an emerging growth company, indicate by check mark if the registrant has elected not to use the extended transition period for complying with any new or revised financial accounting standards provided pursuant to Section 13(a) of the Exchange Act. ☐

Item 5.07 Submission of Matters to a Vote of Security Holders.

On May 27, 2025, OnKure Therapeutics, Inc. (the “Company”) held its 2025 Annual Meeting of Stockholders (the “Annual Meeting”). At the Annual Meeting, the Company’s stockholders voted on the two proposals set forth below. A more detailed description of each proposal is set forth in the Company’s Proxy Statement filed with the Securities and Exchange Commission on April 16, 2025.

Proposal No. 1: Election of Directors

Drs. Isaac Manke and Nicholas Saccomano were each elected to serve as a Class I director of the Company’s Board of Directors until the 2028 Annual Meeting of Stockholders and until their respective successors are elected and qualified, by the following votes:

Proposal No. 2: Ratification of the Selection of Independent Registered Public Accounting Firm

The stockholders ratified the selection of KPMG LLP as the Company’s independent registered public accounting firm for the fiscal year ending December 31, 2025, by the following votes:

Item 9.01 Financial Statements and Exhibits.

(d) Exhibits.

SIGNATURES

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 hereunto duly authorized.