Two television hosts attacked by Donald Trump have questioned the US President’s mental health and accused him of trying to exert pressure on them over unfavourable coverage.

Mr Trump drew a barrage of criticism, including from his fellow Republicans, after he called Mika Brzezinski, a co-host of the MSNBC Morning Joe program, “low I.Q. Crazy Mika” and said she was “bleeding badly from a face-lift” when she visited his Mar-A-Lago estate around New Year’s Eve.

He referred to her co-host and fiance Joe Scarborough, a former Republican US congressman, as “Psycho Joe”.

The anchors — who were on friendly terms with Mr Trump early in the 2016 presidential campaign but have been critical of him since he took office — responded with a column in The Washington Post on Friday titled: “Donald Trump is not well”.

“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.”

Scarborough told the Morning Joe show he received calls from three top administration officials asking the co-hosts to call Mr Trump and apologise for their coverage of his administration.

They told him that if he called and apologised, Mr Trump would get the story killed, Scarborough said.

“The calls kept coming, and kept coming. And they were like, ‘Call, you need to call. Please call. Come on, Joe. Just pick up the phone and call him’,” Scarborough said.

In a Twitter message on Friday, Mr Trump effectively denied the allegation, giving a different version of what transpired around the National Enquirer piece.

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

— Donald J. Trump (@realDonaldTrump) June 30, 2017

In a response to Mr Trump’s claim Scarborough had called him to get the National Enquirer article stopped, Scarborough tweeted that it was “yet another 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. https://t.co/TZWiElo6Gs

— Joe Scarborough (@JoeNBC) June 30, 2017

There was no immediate comment from the National Enquirer, a tabloid that specialises in scandalous stories about celebrities and has been supportive of Mr Trump.

Trump ‘attacks women because he fears women’

In the Washington Post column, Brzezinski and Scarborough lambasted Mr Trump as mentally unstable, saying he had an “unhealthy obsession” with their television program, and cited what they called his continued mistreatment of women.

Brzezinski, a daughter of former White House national security adviser Zbigniew Brzezinski, said her main concern was how such behaviour affected the country.

“I am very concerned as to what this once again reveals about the President of the United States,” Brzezinski said.

“[Mr Trump] appears to have a fragile, impetuous, child-like ego that we’ve seen over and over again, especially with women.

Scarborough added: “He attacks women because he fears women.”

Mr Trump uses Twitter prolifically and often as a vehicle to attack critics but Thursday’s tweets about the Morning Joe hosts were seen by many as offensive.

Brzezinski and Scarborough dismissed as lies Mr Trump’s Twitter claims that he refused to have dinner with them or that Brzezinski had undergone a face lift.

They also said they had seen a change in the President over the last few years.

“President Trump launched personal attacks against us Thursday, but our concerns about his unmoored behaviour go far beyond the personal,” they wrote in the Washington Post column.

“America’s leaders and allies are asking themselves yet again whether this man is fit to be president.”

— with agencies