Carl Bernstein is rallying reporters to investigate "how pervasive" talk is among top Republicans and members of the military about President Trump's ability to lead.

"Important Republicans/conservs/Intel-military hi-ups increasingly saying in private that @realDonaldTrump is unfit to be president [because] of lack of ethics, competence, ‘temperament/stability,'" Bernstein tweeted Tuesday afternoon.

"Reporters should find out how pervasive such talk may be," he added.

His tweets Tuesday echo what he said Monday evening on "CNN Tonight," when he said the president's Charlottesville reaction posed a "journalistic question" that should be pursued.

Bernstein said that Trump's initial reluctance to condemn, by name, the groups behind this weekend's violent white supremacy rally in Charlottesville, Va., represented a "demarcation line that we're going to remember for a long time because the rules have now changed."

Bernstein, best known for his investigative reporting that shed light on the Watergate scandal leading to former President Richard Nixon's resignation in 1974, alleged that the optics of Trump's hesitation to condemn these groups, some of which praised Trump's first reaction, are grounds for Trump losing his chance to lead the entire nation effectively.

"He's the president of his base, but there's very little proof now that he is president of all the American people and that he can bring them together or that he can continue in a way that serves him to continue as president in an effective way because of how people are talking about him," Bernstein said.

Trump's attacks on the GOP leadership, particularly Senate Majority Leader Mitch McConnell last week, have also divided the party, with several members publicly defending the Kentucky Republican.