President Donald Trump lashed out at former CIA Director John Brennan after Brennan criticized Mr. Trump for remarks he made during a joint press conference with Russian President Vladimir Putin.

"I think Brennan is a very bad guy, and if you look at it, a lot of things happened under his watch," Mr. Trump said in an interview with Fox News' Tucker Carlson in Helsinki on Monday. "I think he's a very bad person."

Brennan had previously called Mr. Trump's press conference remarks "nothing short of treasonous."

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"Donald Trump's press conference performance in Helsinki rises to & exceeds the threshold of 'high crimes & misdemeanors,'" Brennan tweeted on Monday. "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???"

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??? — John O. Brennan (@JohnBrennan) July 16, 2018

Brennan said on the "Today" show, "When I use the term, this is 'nothing short of treasonous,' I equate it to the betrayal of one's nation, aiding, abetting, giving comfort to an enemy." The president had the chance to warn Putin, to tell him, "'Do not do this again,' and he failed to even meet the minimum standards of that," Brennan continued.

In the joint news conference on Monday that followed a day of discussions between the two leaders in Helsinki, Finland, Mr. Trump stood next to Putin and defended him in the face of the conclusion by all the U.S. intelligence agencies that the Russian government directed cyberattacks on the Democratic Party and on the campaign of its 2016 nominee, Hillary Clinton. The intelligence assessment also said that Putin and the Russian government "aspired to help President-elect Trump's election chances when possible by discrediting Secretary Clinton and publicly contrasting her unfavorably to him."

"Dan Coats came to me," the president said, mentioning the director of national intelligence, "and some others, they said they think it's Russia. I have President Putin -- he just said it's not Russia. I will say this, I don't see any reason why it would be."

During his interview with Carlson, which airs Tuesday night, Mr. Trump also brought up FBI investigator Peter Strzok and former FBI lawyer Lisa Page, whose anti-Trump texts during probes into both Hillary Clinton's email server and Russian meddling in the 2016 election have been examined in congressional investigations and a report by the Justice Department's inspector general.

"I also think that when you watch Peter Strzok and Lisa Page, when you watch all of the things that have happened -- Comey, you take a look at that and McCabe who has got some pretty big problems I assume, you look at the deception, the lies. ... These are people that in my opinion are truly bad people, and they're being exposed for what they are."