WASHINGTON—U.S. prosecutors have filed criminal charges against National Security Agency leaker Edward Snowden and asked Hong Kong authorities for his provisional arrest, kicking off what is expected to be a lengthy process to seek his transfer to the U.S.

A one-page criminal complaint, filed in U.S. District Court in Alexandria, Va., accused Mr. Snowden of theft of government property and willful communication of classified communications intelligence to an unauthorized person.

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