The co-hosts of a US morning talk show have struck back at abusive tweets from President Donald Trump.

Joe Scarborough and Mika Brzezinski claimed Mr Trump lied about a previous encounter in a tweet and said his “unhealthy obsession” with their Morning Joe programme does not serve his mental health or the country well.

The two MSNBC personalities postponed a holiday to respond to Mr Trump’s tweet, which drew broad condemnation after he called Ms Brzezinski “crazy” and claimed she was “bleeding badly from a face-lift” when he saw them at his Florida estate in December.

“It’s been fascinating and frightening and really sad for our country,” she said on the programme.

“We’re okay,” said Mr Scarborough, her co-host and fiance. “The country’s not.”

The hosts, who also published a column on the Washington Post website on Friday, said they had known Mr Trump for more than a decade and had “fond memories” of their relationship, but that he has changed in the past two years.

They visited his Mar-a-Lago estate in Florida in late December to encourage Mr Trump to give them an interview.

Ms Brzezinski, who said she is alarmed at how the president deals with women who disagree with him, added that she believes her teasing about a Washington Post story about fake Time magazine covers with Mr Trump’s face hanging at his golf facilities is what precipitated the latest Twitter attack.

“It is unbelievably alarming that this president is so easily played, he is easily played by a cable news host,” she said.

“What does that say to our allies? What does that say to our enemies?”

After Mr Trump’s initial tweets, Ms Brzezinski responded on Twitter by posting a photograph of a cereal box that includes the phrase “made for little hands”.

Critics looking to get under the president’s skin have long suggested that his hands appear smaller than usual for his frame.

The duo went on to say Mr Trump was lying about Ms Brzezinski having a face-lift, although “she did have a little skin under her chin tweaked”.

Their programme and Mr Trump have had a chequered relationship. They were criticised by some for being too close to him during the election campaign and giving his candidacy an early boost, but have turned sharply against him.

Ms Brzezinski in recent weeks has wondered whether Mr Trump was mentally ill and said the country under his presidency “does feel like a developing dictatorship”.

The hosts said they have noticed a change in his behaviour over the past few years which left them neither shocked nor insulted by the Thursday tweet.

“The guy who is in the White House now is not the guy we know,” Mr Scarborough said.

Mr Trump on Thursday launched a crude attack on Ms Brzezinski, tweeting: “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!”

The tweets united Democrats and Republicans in a chorus of protest that amounted to perhaps the loudest outcry since Mr Trump took office.

“Obviously I don’t see that as an appropriate comment,” said Republican House Speaker Paul Ryan.

House Speaker Paul Ryan said: “Obviously I don’t see that as an appropriate comment.”

Republican Representative Lynn Jenkins said on Twitter: “This is not okay. As a female in politics I am often criticised for my looks. We should be working to empower women.”

House Democratic leader Nancy Pelosi called Mr Trump’s tweets, “blatantly sexist”. The president, she added, “happens to disrespect women… it’s sad”.