Investigative reporter Carl Bernstein says the task of reporting on President Trump's fitness for office is a challenge for journalists.

"We're in a real constitutional crisis, in an unprecedented place, where we as a country and where we as journalists, have never been before, in which a huge part of the citizenry of our country and the leadership of the country in Congress, privately and in public, openly question the fitness and stability of the president of the United States," Bernstein told CNN's Brian Stelter on "Reliable Sources" Sunday.

He added: "So it raises a great question: How do we report on this reality?"

Bernstein, a CNN contributor, urged journalists to dig in to the topic. While he suggested that all outlets should report on the issue, he also singled out the conservative Fox News -- the president's favorite channel.

"This is a great challenge for Fox News because they have the kind of credibility with Republicans in Congress that perhaps other news organizations don't have," Bernstein said. "This is a chance to show that they can be fair and balanced."

Questions about Trump's fitness for office have been circulating for months. One Democratic member of Congress even introduced a bill that would use the 25th Amendment of the Constitution to create a "body" to determine whether Trump is unable to do his job.

The amendment establishes procedures for replacing the President or Vice President in the event of death, removal, resignation or incapacitation.

Bernstein has said for months that many people privately question Trump's ability to serve. He said Sunday that he has talked to "many Republicans in Congress."

Discussion about the topic exploded last week after the release of Michael Wolff's new book, "Fire and Fury: Inside the Trump White House." It paints the president as someone who neither knows nor cares about policy and doesn't seem to perceive the vast responsibilities of his role.

Related: Bernstein says this is the Trump story reporters need to cover

Some details in the book have been corroborated, while others have been debunked. CNN has not independently verified all the book's details.

Trump allies staunchly deny that questions about Trump's mental fitness hold any merit.

White House Press Secretary Sarah Sanders said last week that such questions are "disgraceful and laughable." Secretary of State Rex Tillerson said he's "never questioned" the president's mental fitness.

Trump took to Twitter on Saturday in his own defense. He said he's a "very stable genius" who is "like, really smart."

Bernstein -- who is best known for partnering with Bob Woodward to report on the Watergate scandal that toppled President Richard Nixon in the 1970s -- said reporters need to start talking to members of Congress about their personal views on the subject.

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"All of these news organizations need to be flooding the Hill with reporters who ask every single Republican member of the House and Senate, what do you really think?" he said. "And come back to the American people as viewers and readers with what their reporting shows."

Indira Lakshmanan, the ethics chair at the Poynter Institute, a journalism advocacy group, agreed that it is a worthwhile subject. But she also cautioned that it can be "politicized."

"How do you write it in a way so that you don't fall into the president's so-called 'enemies of the people' trap?" she asked, adding that it's important for journalists to tackle the topic in a "clear-eyed way."