UNITED STATES SECURITIES AND EXCHANGE COMMISSION

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Washington, D.C. 20549

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FORM 6-K

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REPORT OF FOREIGN PRIVATE ISSUER

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

THE SECURITIES EXCHANGE ACT OF 1934

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For the month of April, 2025

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Commission File Number: 001-40709

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Ardagh Metal Packaging S.A.

(Name of Registrant)

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56, rue Charles Martel

L-2134 Luxembourg, Luxembourg

+352 26 25 85 55

 (Address of Principal Executive Office)

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Indicate by check mark whether the registrant files or will file annual reports under cover of Form 20-F or Form 40-F.

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Form 20-F  ☒        Form 40-F  ☐

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INFORMATION CONTAINED IN THIS REPORT ON FORM 6-K

This report on Form 6-K comprises of Ardagh Metal Packaging S.A.’s (the “Company”) press release on the update provided by Ardagh Group S.A. (“AGSA”) on its discussions with AGSA’s noteholders on April 7, 2025, which is attached hereto as Exhibit 99.1 and its previous press release on the update on March 11, 2025, which is attached hereto as Exhibit 99.2.

Incorporation by Reference

The information set forth in this report on Form 6-K shall be deemed to be incorporated by reference into the registration statement filed on Form F-3, as amended (Registration No. 333-258749) by the Company (including any prospectus forming a part of such registration statement), and to be a part thereof from the date on which this report is furnished, to the extent not superseded by documents or reports subsequently filed or furnished.

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EXHIBIT INDEX

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SIGNATURES

Pursuant to the requirements of the Securities Exchange Act of 1934, Ardagh Metal Packaging S.A. has duly caused this report to be signed on its behalf by the undersigned, thereunto duly authorized.

Date:    April 7, 2025

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