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

For the month of June 2026

Commission File Number 001-42254

Rezolve AI plc

(Translation of registrant’s name into English)

21 Sackville Street,

London, W1S 3DN

United Kingdom

(Address of principal executive offices)

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 REPORT ON FORM 6-K

On June 30, 2026, Rezolve AI plc (the "Company") issued a press release announcing that Company shareholders have approved the capital reduction and share repurchase authority required to launch a buyback program of up to $300 million. A copy of the press release is furnished as Exhibit 99.1 to this Report on Form 6-K and is incorporated herein by reference.

The information included in this report on Form 6-K, including Exhibit 99.1, is being furnished and shall not be deemed "filed" for purposes of Section 18 of the Securities Exchange Act 1934, as amended (the "Exchange Act"), or otherwise subject to the liabilities of that section, nor shall it be deemed incorporated by reference in any filing under the Securities Act of 1933, as amended, or the Exchange Act, except as otherwise set forth herein or as shall be expressly set forth by specific reference in such filing.

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 hereunto duly authorized.

Dated: June 30, 2026