Joe Scarborough and Mika Brzezinski on "Morning Joe." MSNBC

"Morning Joe" cohosts Mika Brzezinski and Joe Scarborough have responded to President Donald Trump's tweets attacking the pair.

In a Washington Post column published early Friday titled "Donald Trump is not well," Brzezinski and Scarborough wrote "we are both certain" that Trump "is not mentally equipped to continue watching our show."

In tweets Thursday morning, the president called the two "low I.Q. Crazy Mika" and "Psycho Joe." Trump also claimed Brzezinski once visited his Florida estate, Mar-a-Lago, while she was "bleeding from a face-lift."

"I heard poorly rated @Morning's 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," Trump tweeted. "She was bleeding badly from a face-lift. I said no!"

On "Morning Joe" on Friday morning, Brzezinski said, "I'm fine. My family brought me up really tough."

The tweet "doesn't bother me one bit," she said.

Scarborough went further, saying, "We're OK — the country is not."

In Friday's Washington Post column, Brzezinski and Scarborough responded to specific claims Trump made in his tweets.

"Mr. Trump claims that we asked to join him at Mar-a-Lago three nights in a row. That is false. He also claimed that he refused to see us. That is laughable," Brzezinski and Scarborough wrote.

"Mr. Trump also claims that Mika was 'bleeding badly from a face-lift.' That is also a lie."

The column cites pictures from the night showing that "Mika and her face were perfectly intact." CNN's Brian Stelter posted a photo of Brzezinski from the Mar-a-Lago visit in which she looks uninjured:

Brzezinski originally responded to Trump's tweets Thursday by tweeting a photo of a box of Cheerios featuring the words "Made For Little Hands." For years, Trump has taken issue with people saying he has small hands and fingers.

The White House deputy press secretary, Sarah Huckabee Sanders, argued Thursday that the president had every right to "hit back" at "the liberal media" and "Hollywood elites" when they criticize him.

The segment that may have triggered Trump's tweeting Thursday morning took aim at a fake Time magazine cover that The Washington Post had learned was hanging at several of Trump's golf clubs and properties.

"Nothing makes a man feel better than making a fake cover of a magazine about himself lying every day and destroying the country," Brzezinski said.

Brzezinski also said Trump was covering his hands on the fake Time cover "because they're teensy."

Top Republicans denounced Trump after the tweets.

"Obviously, I don't see that as an appropriate comment," House Speaker Paul Ryan said. "What we're trying to do around here is improve the tone and the civility of the debate, and this obviously doesn't help do that."

Trump has had a contentious relationship with the MSNBC hosts. Before Trump ran for president, Brzezinski and Scarborough were friendly with him, and they were initially receptive to his candidacy.

But they have since pivoted to criticizing him heavily on-air. In turn, Trump has both praised the pair and criticized them on social media since announcing his candidacy in 2015.

An MSNBC representative told Business Insider,"It's a sad day for America when the president spends his time bullying, lying, and spewing petty personal attacks instead of doing his job."

Allan Smith contributed to this report.