MSNBC's Mika Brzezinski and Joe Scarborough said Friday that White House officials threatened to arrange for negative news coverage against them if they did not tone down their criticism of President Donald Trump.

Speaking a day after Trump's Twitter blast against the "Morning Joe" co-hosts, they said the threat involved a damaging story in the National Enquirer. Trump is friendly with David Pecker, CEO of the tabloid's parent company American Media Inc.

"They were calling my children, they were calling close friends of mine, and they were pinning the story on my ex-husband who would absolutely never do that," Brzezinski said. "So I knew immediately it was a lie and they had nothing. These calls persisted for quite some time."

Scarborough said three people "at the very top of the administration" urged him repeatedly to call the president. Later, he continued, he was at Brzezinski's house and saw "a tabloid guy." Scarborough said the person told him to call the president.

Brzezinski said she and Scarborough discussed the situation and decided against calling Trump. The National Enquirer later ran a story about Scarborough buying beer at a convenience store, which Scarborough said Friday was false.

The tabloid's website also published a story on June 2 that said Brzezinski and Scarborough had been having an affair with each other while being married to other people. The story was leading its site on Friday. Neither "Morning Joe" host acknowledged it on Friday. They announced their engagement in May.

On Twitter on Friday, Trump blasted the pair again.

Watched low rated @Morning_Joe for first time in long time. FAKE NEWS. He called me to stop a National Enquirer article. I said no! Bad show

Scarborough called Trump's tweet a "lie."

Yet another lie. I have texts from your top aides and phone records. Also, those records show I haven't spoken with you in many months.

The National Enquirer did not immediately respond to a CNBC request for comment.

Politico's Hadas Gold tweeted on Friday that MSNBC is not planning to immediately release the correspondence between Scarborough and the White House alleged by Scarborough.

MSNBC says they are not planning right now to release the convos btwn Joe and WH officials as proof

Scarborough said the National Enquirer story is emblematic of Trump's "really strange obsession" with "Morning Joe" and his "really disturbing obsession with Mika."

Brzezinski and Scarborough made their comments one day after Trump tweeted: "I heard poorly rated @Morning_Joe speaks badly of me (don't watch anymore). Then how come low I.Q. Crazy Mika, along with Psycho Joe, came …. to Mar-a-Lago 3 nights in a row around New Year's Eve, and insisted on joining me. She was bleeding badly from a face-lift. I said no!"

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Trump's tweets drew widespread criticism from Republicans and Democrats. Scarborough and Brzezinski published an op-ed in The Washington Post on Friday titled "Donald Trump is not well."

The two said they are not personally hurt by Trump's Twitter attack, but they are worried for the country.

"This appears to be a man who cannot take the tiniest tweak from a woman on cable news but requires his Cabinet to speak at length about his greatness, especially in the middle of a presidency that appears to be struggling, low approval ratings and very few accomplishments," Brzezinski said. "He's not in reality."

They said they worry what the president's outbursts show the rest of the world.

"Think about it," Brzezinski said. "It's unbelievably alarmingly this president is so easily played, so unbelievably played by a cable news host. What is that saying to our allies? What is that saying to our enemies? That our president is so easily played."

Brzezinski and Scarborough, told more of their story in an interview with Vanity Fair that was published Friday.

Scarborough, a lifelong Republican, said Trump's actions are especially frustrating because they take the focus off issues like health care, tax reform and infrastructure. And, he said, it only deepens the partisan divide two weeks after Rep. Steve Scalise was severely wounded in a shooting at a congressional Republican baseball team practice.

Disclosure: MSNBC and CNBC are owned by NBCUniversal.