CNN ran a news segment asking if Donald Trump is fit for office after his reaction to the neo-Nazi rally in Charlottesville.
Introducing a panel on CNN's "Reliable Sources," Brian Stelter said Mr Trump's "actions and inactions in the wake of Charlottesville are provoking some uncomfortable conversations."
He said the US President's actions raised several questions, such as: "Is the President of the United States a racist? Is he suffering from some kind of illness? Is he fit for office?
"And if he is unfit, then what?"
Carl Bernstein, the famed Watergate journalist, went on to call on journalists to follow the "important, crucial, dangerous story" of doubts among Republicans over Mr Trump's fitness for office.
He said he had spoken to many sources who had been "raising the very question of his stability and his mental fitness to be President".
Mr Bernstein said: "Republicans in Congress, the highest of intelligence officials, the highest of military officers in our country, leaders of the business community, all of whom have dealt with the White House, and many of them dealt personally with Donald Trump, have come to believe that he is unfit for the presidency.
"That's what I'm learning as a reporter talking to many, many people in Washington, who over the last month or two have come to that conclusion.
"And especially among Republicans in Congress, they have been raising the very question of his stability and his mental fitness to be President of the United States."
He added that journalists "need to start making their business" to report on the "important, crucial, dangerous" story.
Several Republicans have openly asked whether Mr Trump is fit to be President, including Senator Bob Corker, who said Mr Trump had not demonstrated "the stability nor some of the competence" to succeed in the role.