Top White House aides said they would prevent a tabloid newspaper from publishing a negative story about MSNBC hosts Mika Brzezinski and Joe Scarborough if they apologised to Donald Trump , the TV presenters have alleged.

Brzezinski and Scarborough made the blackmail allegations in an article jointly written for the Washington Post .

"This year, top White House staff members warned that the National Enquirer was planning to publish a negative article about us unless we begged the president to have the story spiked," they wrote.

"We ignored their desperate pleas."

Trump denied the pair's blackmail claims in a tweet sent out hours ago.

"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," Trump tweeted.

Scarborough issued a quick reply.

"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," Scarborough tweeted.

"Why do you keep lying about things that are so easily disproven? What is wrong with you?"

The National Enquirer, a tabloid newspaper known for its lurid content, denied involvement in any discussions between the White House and the MSNBC hosts.

"At no time did we threaten either Joe or Mika or their children in connection with our reporting on the story," the vice-president of the Enquirer's publisher said.

The pair, who are engaged to be married, also denied Trump's claims that Brzezinski was "bleeding badly from a face-lift" when she visited Mar-a-Lago in December.

"Putting aside Mr. Trump’s never-ending obsession with women’s blood, Mika and her face were perfectly intact, as pictures from that night reveal," Scarborough and Brzezinski wrote.

"And though it is no one's business, the president’s petulant personal attack against yet another woman’s looks compels us to report that Mika has never had a face-lift.

"If she had, it would be evident to anyone watching 'Morning Joe' on their high-definition TV."

Brzezinski and Scarborough were scheduled to go on vacation yesterday, but appeared on their show to address Trump's tweets.

"He appears to have a fragile, impetuous, childlike ego that we have seen over and over again — especially with women. He can't take it," Brzezinski said.

Scarborough, a former Republican congressman, has been a vocal Trump critic for much of his presidency.

He and Brzezinski were two of about 40 people Trump followed on Twitter, but the president unfollowed them recently.

Trump attacked Scarborough and Brzezinski on Twitter on Thursday morning, shortly after the pair mocked the fake Time magazine cover hanging on the walls of several of his golf clubs.

"I heard poorly rated Morning Joe speaks badly of me (don't watch anymore)," he tweeted.

"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!"

Trump's tweets were roundly criticised by politicians from both parties, with Republican senators Ben Sasse, Lisa Murkowsi, James Lankford and Susan Collins all slamming the president's attack.