Michael Rogers says some terrorists have made changes to the way they communicate but talks down damage from revelations

The new director of the National Security Agency, Admiral Michael Rogers, has played down the damage caused by Edward Snowden's revelations – in contrast to claims by his predecessor and British counterparts that it was one of the worst breaches in intelligence history.

Rogers said in an interview with the New York Times that some terrorists had made changes in the way they communicate as a result of the revelations focusing on the US spying communications agency, but overall he had concluded the sky was not falling.

His predecessor, General Keith Alexander, described the leak of tens of thousands of documents from the NSA and British counterpart GCHQ – as well as the surveillance agencies of Australia, New Zealand and Canada – as "the greatest damage to our combined nations' intelligence systems that we have ever suffered". British intelligence has spoken of areas of the world having "gone dark" and of disruption caused to intelligence-gathering.

The outgoing head of MI6, Sir John Sawers, giving evidence to a parliamentary committee, said Britain's enemies were rubbing their hands with glee and "al-Qaida is lapping it up".

Rogers said the agency had overheard terrorist groups "specifically referencing data detailed" by Snowden's revelations. "I have seen groups not only talk about making changes, I have seen them make changes," he said. But he added: "You have not heard me as the director say, 'Oh, my God, the sky is falling.' I am trying to be very specific and very measured in my characterisations."

He said that one of the biggest changes was that the NSA had taken steps to try to ensure that never again could a single individual accumulate so much documentation and walk away with it as Snowden had done. He added, though, that there was no such thing as total security.

"Am I ever going to sit here and say as the director that with 100% certainty no one can compromise our systems from the inside?" he asked. "Nope. Because I don't believe that in the long run."

One of the biggest revelations in the Snowden documents was the relationship between the security agencies and private telecom and internet companies, which have suffered from consumer backlashes as a result. Rogers acknowledged that the relationship with the companies, previously kept largely from the public, had changed, probably forever.

The companies were saying they would now have to be compelled to hand over information, he said, rather than hand it over voluntarily.

He confirmed that the Obama administration had told the NSA to stop monitoring some foreign leaders including the German chancellor, Angela Merkel.

"There are some specific targets where we've been instructed, 'Hey, don't collect against them anymore,' " he said. He declined to say how many beyond noting, "probably more than half a dozen, but not in the hundreds by any means".

Intelligence agencies in both the US and UK have been inconsistent in their response to the Snowden revelations, variously describing him as being a Chinese spy, having had documents snatched by Beijing agents, working for the Russians or having done a deal with the Kremlin.

Snowden handed the documents to the Guardian and the Washington Post, which both began publishing them in June last year, starting a worldwide debate on surveillance and privacy.

Since taking over, Rogers has said the NSA will have to be more transparent in order to restore public trust and acknowledged that, unlike his predecessors, he would have to engage in public debate about the agency's role. In one of his first public comments, early in June, he rejected claims made by others in US and British intelligence that Snowden was working for the Chinese, Russian or any other foreign spy agency.

In his interview with the New York Times, Rogers admitted that the US might have to use cyber weapons against adversaries, with cyber weapons part of the US armoury in much the same way as drones or cruise missiles. One of the early leaked Snowden documents included a White House policy document showing that US cyber weapons were not, as the US had declared, primarily for defensive purposes but offensive ones too.

On steps taken to try to avoid another Snowden, Rogers outlined security measures that include two people, rather than one, being needed to access sensitive data.