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The House Judiciary Committee’s ranking Democrat, Rep. John Conyers of Michigan, told Mr. Mueller that the surveillance programs reach too far.

“We are on the verge of becoming a surveillance state,” he said Thursday during a hearing.

“It seems clear that the government’s activity exceeds the authority this Congress has provided, both in letter and in spirit,” said Mr. Conyers, adding that he would introduce legislation Friday to impose restrictions and new oversight for surveillance programs.

Mr. Mueller attempted to assure lawmakers that the programs are limited, court-approved and overseen by Congress.

“The legality has been assured by the Department of Justice,” Mr. Mueller said in his final scheduled appearance before Congress before he leaves office this year. He added that the Foreign Intelligence Surveillance Court “has ruled on these two programs, monitors these two programs and has assured the legality of the efforts undertaken in these two programs.”

Top-secret documents about the two programs were posted online last week after being leaked to the news media by Mr. Snowden, a self-proclaimed whistleblower. One program involves the collection of telephone “metadata” about every U.S. phone call — information about who was calling whom, when and for how long.

Rep. Jason Chaffetz, Utah Republican, asked Mr. Mueller whether metadata included location information — records of where the telephone was when a call is made.

“That’s a question I’d have to get back to you on. I had not thought about that,” Mr. Mueller said.

Mr. Chaffetz noted that he had submitted his questions in advance, “so I could have a candid dialogue with you.”

“It’s terribly frustrating, sir,” he said after Mr. Mueller promised to get back to him with the information. “This is an important discussion and dialogue, and I know I won’t get an answer.”

Among congressional members and staffers, the FBI has long been notorious for taking an inordinate length of time to respond to questions for the record arising out of the director’s annual testimony.

Mr. Mueller promised Mr. Chaffetz that he would meet with him personally to answer what he said are “complex” questions about location data.

The Supreme Court recently held that a warrant should be required for police to attach a tracking device to a vehicle, but as Mr. Chaffetz pointed out, that would not be necessary if suspects could be tracked using their phone records.

Jerry Seper contributed to this article, which is based in part on wire service reports.