WASHINGTON -- Deputy Attorney General Rod Rosenstein discussed secretly recording U.S. President Donald Trump last year as law enforcement agencies grew increasingly unnerved about chaos in the White House, according to people familiar with the exchange. One person who was present at the time said Rosenstein was just being sarcastic.

Trump spoke later Friday of a "lingering stench" at the Justice Department, though he didn't name names. But the reports add fuel to Trump's longstanding claims that his law enforcement agencies are biased against him and determined to undermine his presidency.

Rosenstein's comments were first reported Friday by The New York Times. The Times also said Rosenstein raised the idea of using the 25th Amendment to remove Trump as unfit for office.

Rosenstein issued a swift denial.

"I never pursued or authorized recording the President and any suggestion that I have ever advocated for the removal of the President is absolutely false," he said.

The reports create even greater uncertainty for Rosenstein in his position at a time when Trump has lambasted Justice Department leadership and publicly humiliated both him and Attorney General Jeff Sessions.

It's also the latest revelation that could affect Robert Mueller, the special counsel investigating possible co-ordination between Russia and Trump's presidential campaign in 2016. Sessions recused from that issue soon after he took office, to Trump's dismay, and Rosenstein later appointed Mueller. With all that hanging in the air, Trump has resisted calls from conservative commentators to fire both Sessions and Rosenstein and appoint someone who would ride herd more closely on Mueller or dismiss him.

The reported conversation about possibly secretly recording the president took place at a tense May 2017 meeting during the tumultuous period that followed Trump's firing of FBI Director James Comey, a decision that upset many rank-and-file agents and that the White House said was based on the Justice Department's recommendation.

Among the participants was Andrew McCabe, the FBI official who was temporarily elevated to director after Comey's firing and who documented conversations with senior officials, including Rosenstein, in memos that have been provided to Mueller as part of his investigation.

The interactions lay bare the conflicts that roiled the FBI and Justice Department early in the Trump administration after Rosenstein, just weeks into his job, wrote a memo critical of Comey's handling of the Hillary Clinton email server investigation that the White House used as justification for firing the FBI director.

Friday's news reports threatened to cloud Rosenstein's fate at the Justice Department, with some conservatives calling for him to be fired immediately. Any dismissal could affect Mueller's Russia probe given that Rosenstein still oversees Mueller's work.

Trump told a campaign rally in Missouri that the department has some "great people" but also "some real bad ones." He said the bad ones are gone, "but there's a lingering stench and we're going to get rid of that, too." It was unclear to whom he was referring.

It was difficult amid the conflicting accounts to discern the precise context of Rosenstein's comments and how they were intended.

The Justice Department, for instance, released an email from one attendee who said Rosenstein's "statement was sarcastic and was never discussed with any intention of recording a conversation with the president."

Rosenstein called the Times story "inaccurate and factually incorrect."

One of the people briefed on the conversation in question, who spoke on condition of anonymity because of the confidential nature of the interaction, said it occurred during a moment of frustration between McCabe and Rosenstein.

Rosenstein was rankled by the revelation that Comey had kept memos about his interactions with the president; McCabe wanted a more aggressive approach toward the White House, the person said.

At that point, Rosenstein said to McCabe something to the effect of, "What do you want, you want me to wear a wire?" according to the person. Rosenstein was asked in the meeting if he was serious, and he said yes, but he did not mean for the wire comment to be taken seriously as a tactic to investigate Trump, the person said.

The person also said that a memo from McCabe describes Rosenstein as referencing the 25th Amendment to the Constitution, which says that a president can be declared "unable to discharge the powers and duties of his office" upon a majority vote of the vice-president and the Cabinet.

But the person said notes and recollections from other attendees at the meeting, including former FBI lawyer Lisa Page, do not include the 25th Amendment reference.

McCabe's lawyer, Michael Bromwich, said in a statement that McCabe had drafted memos to "memorialize significant discussions he had with high level officials and preserved them so he would have an accurate, contemporaneous record of those discussions." He did not address the content of the memos.

Rosenstein has been a target of Trump's ire since appointing Mueller as special counsel last year. He chose Mueller one week after he laid the groundwork for the firing of Comey by writing a sharply critical memo of his performance. The White House initially cited that memo as justification for Comey's firing, though Trump later said said he was thinking about "this Russia thing" when he made the move.

As deputy attorney general, Rosenstein oversees Mueller's work and has made two public announcements of indictments brought by the special counsel -- one against Russians accused of hacking into Democratic email accounts, the other against Russians accused of running a social media troll farm to sway public opinion.

The news elicited a quick response from members of Congress.

Rep. Mark Meadows, a North Carolina Republican who chairs the conservative Freedom Caucus, said in a tweet that "if this story is true, it underscores a gravely troubling culture at FBI/DOJ and the need for FULL transparency."

Senate Democratic leader Chuck Schumer said the Times story "must not be used as a pretext for the corrupt purpose of firing Deputy Attorney General Rosenstein in order to install an official who will allow the president to interfere with the special counsel's investigation."

Associated Press writer Jonathan Lemire in Springfield, Missouri, contributed to this report.