The White House did not respond on Wednesday when asked if Mr. Trump supported imprisoning reporters who publish stories based on leaked material. The president’s press secretary, Sean Spicer, told reporters on Air Force One that Mr. Trump did not believe the Times article “was an accurate representation of that meeting.”

Mr. Trump often derides the coverage of him and his administration, even as he submits to interviews with a variety of journalists, including from news organizations that he attacks. He told graduates at the Coast Guard Academy on Wednesday that “no politician in history has been treated worse or more unfairly” by the media.

But while Mr. Trump’s proposal to Mr. Comey could be construed as a private fit of pique, journalists and press freedom groups said Wednesday that they were alarmed by the possibility that he considered, even casually, enlisting the Justice Department to quash reporting he disliked.

“We’ve been saying there’s a big gap between the president’s rhetoric and actions he can take to undermine the work of the media,” said Joel Simon, executive director of the Committee to Protect Journalists, which often works to aid reporters in countries with autocratic regimes. “That gap has now been closed.”

At the Feb. 14 meeting, Mr. Trump was fixated on a series of damaging leaks about his administration, according to one of Mr. Comey’s associates, who conveyed to The Times the contents of a memo Mr. Comey wrote after the meeting. The topic led Mr. Trump to suggest that Mr. Comey consider putting reporters in prison for disseminating classified information, the associate said.