US President Donald Trump has launched a scathing personal attack against an MSNBC journalist, after she sharply  criticised his administration's dysfunction in a segment on her show.

"I heard poorly rated @Morning_Joe speaks badly of me (don't watch anymore)," Mr Trump wrote, referring to a morning news show featuring Mika Brzezinski and co-host Joe Scarborough.

"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!" Mr Trump tweeted.

The president, an avid cable news watcher, appears to have been responding to comments by Ms Brzezinski during  the 'Morning Joe' programme on MSNBC.

"Everybody in Washington," Ms Brzezinski said, "in the administration, needs to look at this from... a point of view where they're not lobotomised because you're sitting in there and you're so scared of him, and you think you need to suck up to the president."

She said if a boss at NBC - MSNBC's parent company - "started tweeting wildly about people's appearances, bullying people, talking about people in the competition, lying every day, undermining his managers, throwing them under the (bus) - that person would be thrown out.

"It's just not normal behaviour," she said. "In fact, there would be concerns that the person who runs the company is out of his mind."

Ms Brzezinski appeared to be uncowed by Mr Trump's Twitter attack. She responded to his tweet with a post of her own, a photo of a young child reaching for Cheerios cereal.

"Made for little hands," the picture caption read - a taunt that has been levelled against the image-conscious Mr Trump since the days of his candidacy.

Mr Scarborough re-tweeted a comment from CNN reporter Jake Tapper: "This reminds me: how is @FLOTUS's campaign against cyber-bullying going?" it said, referring to First Lady Melania Trump.

Republican Senator Lindsey Graham criticised Mr Trump's comments saying the tweet was "beneath the office" of the President of the United States.

Congresswoman Lynn Jenkins of Kansas also rowed in on the controversy.

Mr Trump was often interviewed on 'Morning Joe' during the 2016 presidential campaign, but as the White House relationship with much of the US media has soured he has recently favoured interviews with right-wing outlets.

Another Republican senator, Ben Sasse, tweeted, "Please just stop. This isn't normal and it's beneath the dignity of your office."

Democrats seized on the remarks as an example of what they view as Mr Trump's sexism.

"Trump's bullying tweets are an attack on women everywhere," Democratic National Committee spokeswoman Adrienne Watson said in a statement.

"From his Twitter slurs to his policies, we have a president who continues to show us he has no regard for women and whose comments demean the office he holds."

The president's tweets created a new distraction as senators in his own party struggled to bridge their differences and agree on major healthcare legislation.

At a briefing, White House spokeswoman Sarah Sanders called it a "false narrative" to portray Mr Trump's remarks as "an attack on a woman" rather than on a critic, adding, "What about the constant attacks that he receives?"

"He's not going to sit back and get attacked by the liberal media, Hollywood elites. And when they hit him, he's going to hit back," Ms Sanders said.

"I don't think it's a surprise to anybody that he fights fire with fire."

Democratic Senator Ed Markey wrote on Twitter: "If you can't stifle the press, then you attack them personally. Today's tweets from Donald Trump are un-presidential and warrant an apology."

Ms Brzezinski is the daughter of the late Zbigniew Brzezinski, who was president Jimmy Carter's national security adviser.

Mr Scarborough is a Republican former congressman who represented a Florida district in the 1990s.