In a Wednesday tweet, Trump called for Scarborough - as well as MSNBC's president, Phil Griffin - to be fired, citing an unfounded conspiracy theory that Scarborough was somehow implicated in the death of an intern in his congressional office in 2001, when he was a United States representative from Florida.
He and his co-host Mika Brzezinski used to be friends with Mr Trump, who regularly called their programme during the early days of his candidacy.
"You can say that's not okay to say, but at this point, it's reality", Brzezinski interjected again.
Scarborough continued and said he would like Trump's cabinet to serve America and not Trump. "You don't represent him, you represent 320 million people, whose lives are literally in your hands, and we are facing a showdown with a nuclear superpower".
The release of the "Access Hollywood" tape, in which Trump bragged about grabbing women by their sexual organs, proved to be a crisis during the campaign, but a number of news outlets, including the New York Times and Washington Post, have reported that the president has since questioned the authenticity of the recording.
Scarborough then addressed Vice President Mike Pence, reminding him that Republican lawmakers would love for him to be president. "You know you don't serve Donald J. Trump". "After the first nuclear missile goes?"
This tweet appears to be a clear reference to the 2001 death of Lori Klausutis, who was a staffer in Joe Scarborough's congressional office. "Is that when it's proper to bring this up in polite society?" And will they terminate low ratings Joe Scarborough based on the "unsolved mystery" that took place in Florida years ago?
Scarborough claimed that Trump was "completely detached from reality".
Trump wrote, "So now that Matt Lauer is gone when will the Fake News practitioners at NBC be terminating the contract of Phil Griffin?"
The day before the co-hosts embarked on their latest speculation about Trump's mental health, the president targeted Scarborough in a tweet.