Mueller said at a U.S. House Judiciary Committee hearing that Snowden, a former National Security Agency contractor, harmed national security when he divulged the secrets.
"As to the individual who has admitted making these disclosures, he is the subject of an ongoing criminal investigation," Mueller said without naming Snowden.
Mueller added: "We are taking all necessary steps to hold the person responsible for these disclosures."
Snowden is believed to be in Hong Kong after flying there last month from Hawaii, where he lived. He has said he plans to request asylum and that he divulged secrets to Britain's Guardian newspaper and the Washington Post because he believed the U.S. surveillance programs were illegal and intrusive.
The U.S. Justice Department has opened a criminal investigation into the alleged disclosure of classified information. It has not revealed any charges or a request to extradite Snowden.
Mueller added his voice to the Obama administration's defense of the surveillance programs, which he said comply in full with U.S. law and with basic rights guaranteed under the Constitution.
The information in a massive government database of daily telephone records has been instrumental in identifying people who sought to harm Americans, Mueller said.
The program collects "no content whatsoever" beyond data such as numbers called and the time and length of calls, he said.
(Reporting by David Ingram and Laura MacInnis; Editing by Vicki Allen and Jackie Frank)