"We have concrete proof that they have already -- terrorists groups and others -- are taking action, making changes, and it's going to make our job tougher," Army Gen. Keith Alexander told a moderator from NBC News at the Aspen Security Forum in Colorado.
Alexander said the leaks created "significant, irreversible damage to our nation."
In addition, the details about NSA electronic surveillance programs that logged U.S. phone calls and intercepted international Internet communications have caused intelligence sources to dry up, Alexander told the conference.
Alexander said it was impossible for the government to listen to every phone call and read every email even if it wanted to, which it doesn't, he said.
He cited the sheer volume of communications -- 114 billion emails, 24 billion text messages and more than 12 billion phone calls worldwide every day.
"We don't have the technical capabilities. We're a foreign intelligence agency," he said.
"To do that, you'd have to have AT&T's and everybody else's networks. We don't. We'd have to go to them. ... We don't own and operate AT&T. We couldn't compel them to listen to those phone calls. That would require a warrant and a probable-cause finding."
The electronic surveillance programs Snowden revealed were court-approved but kept secret for good reasons, Alexander said.
"The purpose of these programs, and the reason we use secrecy, is not to hide from the American people -- not to hide it from you -- but to hide it from those who walk among you who are trying to kill you," he said.
The head of the American Civil Liberties Union told the conference Snowden did America a service.
"Up until Edward Snowden's revelations, the public debate was anemic. There was very little understanding about surveillance and the implications for ordinary Americans. Now it's much more robust," ACLU Executive Director Anthony Romero said.