SECURITIES AND EXCHANGE COMMISSION

Washington, D.C. 20549

FORM 6-K

REPORT OF FOREIGN PRIVATE ISSUER

PURSUANT TO RULE 13a-16 OR 15d-163

UNDER THE SECURITIES EXCHANGE ACT OF 1934

For the month of June 2026

Alterity Therapeutics Limited

(Name of Registrant)

Level 15, 500 Collins Street, Melbourne, Victoria 3000 Australia

(Address of Principal Executive Office)

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 ☐

This Form 6-K is being incorporated by reference into our Registration Statement on Form S-8 (Files No. 333-251073, 333-248980 and 333-228671) and our Registration Statements on Form F-3 (Files No. 333-274816, 333-251647, 333-231417 and 333-250076)

ALTERITY THERAPEUTICS LIMITED

(a development stage enterprise)

The following exhibits are submitted:

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: June 16, 2026