Michael Hayden, the former director of the CIA and the National Security Agency, said spy agency leaders have grounds to resign following President Trump's Monday remarks at a press conference with Russian President Vladimir Putin.

"It’s a personal choice, of course, but what more should it take?" Hayden told the Washington Examiner after Trump openly expressed doubt about whether Russia intervened in the 2016 U.S. election.

"At some point very senior officials have to decide when they have stopped being a guard rail and when their presence is now merely an enabler and legitimizer. That is the question they must answer," he said. "To be fair, that is very hard question. But sooner or later one has to ask what message staying on sends to the general American public and to the rest of the world."

Hayden led the NSA from 1999 to 2005 and led the CIA under former President George W. Bush from 2006-2009. Although he last worked in a Republican administration, Hayden has described himself as a lifelong political independent.

Hayden said only high-level intelligence agency officials should consider resigning. "[Lower-level] professionals need to stay in place to continue to defend the republic in troubled times," he said.

The U.S. intelligence community concluded in a January 2017 assessment that Russia interfered in the 2016 election, and last week federal prosecutors indicted 12 Russian officials accused of hacking Democratic emails.

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Hayden frequently is critical of Trump. Earlier this year, he released the book The Assault on Intelligence: American National Security in the Age of Lies. But Hayden's critiques pale in comparison to Obama-era CIA director John Brennan's strident denunciations.

Brennan wrote on Twitter: "Donald Trump’s press conference performance in Helsinki rises to & exceeds the threshold of ‘high crimes & misdemeanors.’ It was nothing short of treasonous. Not only were Trump’s comments imbecilic, he is wholly in the pocket of Putin. Republican Patriots: Where are you???"

Hayden does not support Brennan's implicit advocacy of impeachment. "Impeachment or some other steps would look like a coup to 1/3 of America. The proper way to change president is via elections," he said.

It's unclear if any intelligence leaders will resign over Trump's remarks, or if any former intelligence agency leaders will come to Trump's defense. Initial Republican reaction to Trump's remarks has been negative.

A spokesman for the NSA referred a request for comment for NSA Director Paul Nakasone to the Office of the Director of National Intelligence, which is led by Director Dan Coats. ODNI did not immediately respond to the request for comment, nor did spokespeople for the FBI and CIA, who were asked if FBI Director Christopher Wray and CIA Director Gina Haspel had comment.

Standing alongside the Russian leader, Trump said, "my people came to me, Dan Coats came to me and some others saying they think it's Russia. I have President Putin, he just said it is not Russia. I will say this, I don't see any reason why it would be."

Trump also said, "I have great confidence in my intelligence people but I will tell you that President Putin was extremely strong and powerful in his denial today."