Senator John McCain has called for Keith Alexander to "resign or be fired" as the head of the National Security Agency, in an interview with the German news weekly Der Spiegel published on Sunday.

The senator for Arizona, a former Republican presidential candidate, said Alexander should be held accountable for the leaks of thousands of documents by the whistleblower Edward Snowden, which revealed NSA surveillance and spying on a massive scale. McCain said Snowden, who worked for the NSA as a contractor, should never have had access to classified information.

"And now we have a contractor employee, not a government employee, who has access to information which is, when revealed, most damaging to the standing prestige of the United States and our relations with some of our best friends," McCain said. "Why did Edward Snowden have that information? And what are we doing as far as screening people who have access to this information? It's outrageous, and someone ought to be held accountable."

President Barack Obama, the NSA and the congressional intelligence committee had responsibility for the sharing of classified information, he said.

Asked if Alexander should resign, McCain said: "Of course, he should resign, or be fired. We no longer hold anybody accountable in Washington."

Asked if the US intelligence services were out of control, McCain said: "There's not been sufficient congressional oversight, and there has been an absolutely disgraceful sharing of information that never should have taken place. For many years, we had an absolute provision that any classified information, which was going to be shared, is based on need-to-know information."

McCain also spoke to the news weekly about reports, prompted by research by the magazine, that the US had been monitoring the cellphones of German chancellor Angela Merkel and other European leaders. He said it was "conceivable" President Obama had not known about the German chancellor's phone being monitored, but added that he should have.

"Knowing how angry Angela Merkel was, he should have apologized," said McCain. "You know, I've had to do that on numerous occasions in my life. The pain doesn't last very long."

He was asked about whether the US was a real friend of Germany, following revelations that Merkel's phone had been monitored.

McCain said: "Friends spy on friends. We all know that, but there have been certain boundaries. Those boundaries were probably, to some degree, there because we didn't have the capabilities we have now. But when you go to the point where you invade someone's privacy, the leader of certainly Europe, if not one of the most foremost leaders in the world, Angela Merkel, then it was a mistake."

Edward Snowden has reportedly found work in Russia. Photograph: AP

The interview moved to recent discussions in Germany over the possibility of granting asylum to Snowdon, who is currently in Russia. McCain said he did not believe it would happen. "We're too good of friends," he said.

He said he believed Snowden would never return to the US, where he would face trial, even after his asylum in Russia expires at the end of the year.

"[Russian president Vladimir] Putin will grant him asylum indefinitely," McCain said. "The Russians know if they send him back that's a lesson to other people who might defect. I'm sure that Mr Snowden has told them everything that he possibly knows."

Snowden has denied that he has passed information to the Russians, and said he did not take any NSA documents with him. But McCain said: "If you believe that Mr Snowden didn't give the Russians information that he has, then you believe pigs fly."