“So, my personal view is, yes, it’s worth having a conversation about,” Mr. Ledgett told CBS News. “I would need assurances that the remainder of the data could be secured, and my bar for those assurances would be very high. It would be more than just an assertion on his part.”

Mr. Snowden is living and working in Russia under a one-year asylum. The Russian government has refused to extradite Mr. Snowden, who was indicted by the Justice Department in June on charges of espionage and stealing government property, to the United States.

Mr. Snowden has said he would return to the United States if he was offered amnesty, but it is unclear whether Mr. Obama — who would most likely have to make such a decision — would make such an offer, given the damage the administration has claimed Mr. Snowden’s leaks have done to national security.

Because the N.S.A. is still uncertain about exactly what Mr. Snowden took, government officials sometimes first learn about specific documents from reporters preparing their articles for publication — leaving the State Department with little time to notify foreign leaders about coming disclosures.

With the security agency trying to revamp its computer network in the aftermath of what could turn out to be the largest breach of classified information in American history, the Justice Department has continued its investigation of Mr. Snowden.

According to senior government officials, F.B.I. agents from the bureau’s Washington field office, who are leading the investigation, believe that Mr. Snowden methodically downloaded the files over several months while working as a government contractor at the Hawaii facility. They also believe that he worked alone, the officials said.

But for all of Mr. Snowden’s technical expertise, some American officials also place blame on the security agency for being slow to install software that can detect unusual computer activity carried out by the agency’s work force — which, at approximately 35,000 employees, is the largest of any intelligence agency.