Mr. Obama weighed in on the subject in a newly released interview with David Remnick of The New Yorker. He insisted Mr. Snowden had not revealed any illegalities, and though he might have raised “legitimate policy questions” the question was, “Is the only way to do that by giving some 29-year-old free rein to basically dump a mountain of information, much of which is definitely legal, definitely necessary for national security, and should properly be classified?”

Mr. Obama insisted that “the benefit of the debate he generated was not worth the damage done, because there was another way of doing it.” But he did not say what that way was, and even his own aides acknowledge that if Mr. Snowden had not made so much information public, it was doubtful that the president would have announced the reforms and further studies of N.S.A. actions that he spoke about on Friday.

On Sunday, Mr. Rogers appeared to hinge many of his suspicions about Mr. Snowden on a recent Defense Intelligence Agency report that he has described in other interviews as concluding that Mr. Snowden stole about 1.7 million intelligence files that concern vital operations of the United States Army, Navy, Marine Corps and Air Force. He said that it would cost billions of dollars to change operations because of the security breaches.

The defense intelligence report remains classified, though some members of Congress have been briefed on it in recent weeks.

“I don’t think it was a gee-whiz luck event that he ended up in Moscow under the handling of the F.S.B.,” Mr. Rogers said on the NBC program “Meet the Press,” referring to the Federal Security Service, the Russian state security organization that succeeded the K.G.B.

Ben Wizner, an American Civil Liberties Union lawyer who advises Mr. Snowden, said in a telephone interview on Sunday that Mr. Rogers’s statement was “not only false, it is silly.”

Mr. Wizner said that Mr. Snowden’s actions before seeking asylum in Russia were not consistent with someone who was working for a foreign government, pointing out that Mr. Snowden flew to Hong Kong, where he gave classified documents to American journalists. He then sought to travel to Ecuador, and was marooned for five weeks in the transit zone of Moscow’s international airport while he sought asylum in some 20 countries.