UNITED STATES

SECURITIES AND EXCHANGE COMMISSION

Washington, D.C. 20549

FORM 6-K/A

(Amendment No. 1)

REPORT OF FOREIGN PRIVATE ISSUER

PURSUANT TO RULE 13a-16 OR 15d-16

OF THE SECURITIES EXCHANGE ACT OF 1934

For the month of January 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  ☐

Explanatory Note

This Amendment No. 1 to Report of Foreign Private Issuer on Form 6-K (this “Form 6-K/A”) amends the Report of Foreign Private Issuer on Form 6-K (the “Original Filing”) furnished by Rezolve AI plc (the “Company”) to the U.S. Securities and Exchange Commission on January 20, 2026. This Form 6-K/A is being furnished to update Exhibit 10.2 to the Original Filing.

The information included in this Form 6-K/A (including Exhibit 10.2) is hereby incorporated by reference into the Company's Registration Statements on Form F-3 (File No. 333-290523, File No. 333-290639, and File No. 333-291842) and Form S-8 (File No. 333-284174 and File No. 333-292308) (including any prospectuses forming a part of such registration statements) and to be a part thereof from the date on which this Form 6-K/A is furnished.

* Previously filed

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: January 21, 2026