WASHINGTON — President Trump will meet with Rod J. Rosenstein, the deputy attorney general, on Thursday to discuss reports that Mr. Rosenstein talked about invoking the 25th Amendment to remove Mr. Trump from office, Sarah Huckabee Sanders, the press secretary, said on Monday.
The announcement came just hours after the revelation that Mr. Rosenstein was considering resigning, which set off a flurry of speculation about who would replace him at the Justice Department, where Mr. Rosenstein oversees the Russia investigation.
Ms. Sanders, in a statement, said that Mr. Rosenstein and Mr. Trump had “an extended conversation” about the reports — including the fact that Mr. Rosenstein had discussed secretly taping the president. She said the two men will meet on Thursday when the president returns to Washington from New York, where he is attending the United Nations General Assembly.
“I spoke with Rod today, and we’ll see what happens,” Mr. Trump told reporters after Ms. Sanders’s announcement.
Over the weekend, Mr. Rosenstein called a White House official and said he was considering quitting, and a person close to the White House said he was resigning. On Monday morning, after again calling John F. Kelly, the White House chief of staff, to discuss the prospect of his resignation, Mr. Rosenstein headed to the White House to meet with Mr. Kelly.
But Mr. Rosenstein later departed the White House, escorted by Mr. Kelly, with his fate at the Justice Department still unclear.
A departure by Mr. Rosenstein would likely thrust the administration into further turmoil just weeks before November’s midterm elections. As the top Justice Department official overseeing the investigation by Robert S. Mueller III, the special counsel, Mr. Rosenstein had long been the target of Mr. Trump’s bitter grievance about what he calls a politically motivated witch hunt.
Mr. Rosenstein has been a fierce defender of Mr. Mueller, repeatedly refusing to consider firing him despite accusations by Mr. Trump and his allies that the special counsel is part of a Democratic conspiracy to undermine his presidency. His potential departure prompted immediate questions about whether Mr. Trump would seek next to topple Mr. Mueller, a move he tried to orchestrate last year, only to be talked down by his White House counsel.
The turmoil in Washington was heightened by the sense of uncertainty surrounding the specifics of the situation. As reports emerged that Mr. Rosenstein was headed for the White House, Mr. Trump and top aides returned to Trump Tower from meetings at the U.N. to huddle behind closed doors. And Attorney General Jeff Sessions was on a flight back to Washington from Alabama and expected to land early in the afternoon.
The potential changes at the Justice Department exploded into public view even as Brett Kavanaugh, the president’s nominee to the Supreme Court confronted a second allegation of sexual misconduct, roiling the nomination effort on Capitol Hill and prompting Mr. Trump to staunchly defend him.
If Mr. Rosenstein exits, Noel Francisco, the solicitor general, would assume oversight of the Russia investigation, according to a Justice Department official. The acting deputy attorney general would be Matthew G. Whitaker, the chief of staff to Attorney General Jeff Sessions, an unusual move; typically, a top aide to the deputy attorney general would take over the job.
Critics have said that Mr. Francisco, a former lawyer for the Jones Day law firm, cannot oversee the Russia investigation without a waiver from the White House because the firm is representing the Trump campaign in the investigation, creating a conflict of interest. Justice Department officials have not addressed the issue of whether a waiver for Mr. Francisco would be needed if Mr. Rosenstein departs.
It is not known whether Mr. Trump might use the new turmoil at the Justice Department to fire Attorney General Jeff Sessions, a onetime political ally who became the No. 1 target of Mr. Trump’s fury when Mr. Sessions recused himself from overseeing the Russia investigation.
Mr. Rosenstein’s departure would end what had been an often toxic relationship between Mr. Rosenstein and the president that at numerous times left Washington on edge about the potentially drastic consequences for the country if Mr. Trump terminated the deputy attorney general.
In a Twitter rant in April about what he called the “Fake & Corrupt Russia Investigation,” Mr. Trump accused Mr. Rosenstein of being one of the most conflicted members of the Justice Department, asserting that the deputy attorney general was among those who were seeking evidence of a Trump-led conspiracy.
“No Collusion, so they go crazy!” Mr. Trump wrote.
After Mr. Trump refused to express confidence in Mr. Rosenstein in May, the deputy attorney general took a swipe back at the president. During a speech in New York City, Mr. Rosenstein alluded to the verbal beating he had taken from Mr. Trump.
“The dictionary defines ‘piling on’ as joining other people in criticizing someone, usually in an unfair manner — I also have experience with that,” he joked to the audience.
Throughout the summer, Mr. Trump’s allies on Capitol Hill continued to attack Mr. Rosenstein. In July, 11 House lawmakers filed articles of impeachment against him, accusing Mr. Rosenstein of having conflicts of interest when it comes to the Russia investigation. The impeachment effort, which did not have the support of House Republican leaders, made little progress.
But it highlighted the frustration the president and some Republicans have with Mr. Rosenstein’s refusal to accede to their demands to provide documents about the Russia inquiry.
Top Republican lawmakers spent months wrangling over information pertaining to open Justice Department investigations. Democratic opponents have said that those increasing demands were meant to corner Mr. Rosenstein and eventually push him to compromise the integrity of the investigations or to resign.
Mr. Rosenstein has been locked in those increasingly acrimonious negotiations with Representatives Robert W. Goodlatte of Virginia and Trey Gowdy of South Carolina, who run the committees that conduct oversight of the Justice Department; Representative Devin Nunes of California, the chairman of the House Intelligence Committee; and Representatives Mark Meadows of North Carolina and Jim Jordan of Ohio, who lead the House Freedom Caucus — all lawmakers who have close ties to Mr. Trump.
Many of those Republicans have called the Russia investigation into question.
It was Mr. Rosenstein, a 28-year employee of the Justice Department and its No. 2 official, who appointed Mr. Mueller to oversee the investigation last year after it was revealed that Mr. Trump had asked Mr. Comey to quash an inquiry into his former national security adviser.
Mr. Rosenstein himself has overseen Mr. Mueller’s investigation into whether Mr. Trump’s campaign worked with Moscow, and whether the president obstructed justice in the Russia inquiry.
And in April, it was Mr. Rosenstein who personally signed off on the F.B.I. raid on the office and hotel room of Michael D. Cohen, Mr. Trump’s former personal lawyer and longtime confidant, according to government officials. The raids sent the president into a rage in which he complained that the “witch hunt” against him had reached a “whole new level of unfairness.”
The president considered terminating Mr. Rosenstein in summer 2017. In a tweet that June, Mr. Trump complained that he was “being investigated for firing the FBI Director by the man who told me to fire the FBI Director! Witch Hunt.”
Mr. Trump has repeatedly told associates of his frustration with Mr. Rosenstein, according to one official familiar with the conversations, who requested anonymity to discuss personnel matters. The emergence early this year of a memo by congressional Republicans made Mr. Rosenstein’s position even more precarious because it accused him of acting inappropriately when he signed off on the F.B.I.’s request to surveil a former Trump campaign adviser, Carter Page.
The memo described Mr. Rosenstein as one of the senior Justice Department officials who approved an application to extend surveillance of Mr. Page, and it suggested that those applications deliberately avoided mentioning that they were based in part on information in a dossier paid for by Democrats.
But a subsequent memo by Democrats on the House Intelligence Committee undercut those claims, revealing that law enforcement officials had been forthcoming about their sources of the information they cited in seeking permission to surveil Mr. Page.
Conservatives nonetheless seized on the Republican document, which officials at the Justice Department and the F.B.I. said omitted key facts, as grounds for demanding Mr. Rosenstein’s head.
The Tea Party Patriots, a political group, produced a dramatic TV ad calling him “a weak careerist at the Justice Department, protecting liberal Obama holdovers and the ‘deep state’ instead of following the rule of law,” and calling on him to do his job or resign. In April, Mr. Trump lashed out at Mr. Rosenstein for having “signed a FISA warrant,” an apparent reference to Mr. Rosenstein’s role in the surveillance request.
Known as a meticulous lawyer, Mr. Rosenstein began his career at the Justice Department in 1990 as a trial lawyer in the public integrity section of the criminal division in Washington, and rose through the ranks to be nominated in 2005 by President George W. Bush as the United States attorney in Maryland. He held that post for a dozen years, throughout the Obama administration, before being confirmed by the Senate last year as the deputy attorney general.
Within a month, he had been swept into the turmoil surrounding Mr. Comey’s firing when Mr. Trump cited a three-page memo Mr. Rosenstein wrote as a pretext for the sudden dismissal. The memo blamed Mr. Comey’s handling in 2016 of the investigation into Hillary Clinton’s use of a private email server while she was secretary of state.
But Mr. Rosenstein had told lawmakers that he knew that Mr. Comey was to be ousted before he ever sat down to write his memo, and days before, he had spoken with a member of the White House Counsel’s Office about how to handle the matter. Soon after Mr. Comey was fired in May of 2017, Mr. Trump and aides began offering varying explanations, with the president admitting within days that he had made the decision himself as he fumed about the investigation Mr. Comey was leading into his campaign’s ties with Russia.
The day after Mr. Comey’s firing, in an at times tense conversation with Donald F. McGahn II, the White House counsel, Mr. Rosenstein stressed that he did not want to be part of an effort to obfuscate or “massage” the facts about it, according to a person with knowledge of the discussion.
Nearly a week later, The Times reported that Mr. Trump had asked Mr. Comey in February to drop the inquiry into his former national security adviser, Michael T. Flynn, who had misrepresented his communications with Moscow. That suggested that the president was seeking to influence the Russia investigation and raised the specter of obstruction of justice.
The next day, Mr. Rosenstein named Mr. Mueller, a former F.B.I. director, as the special counsel to lead the investigation.
Katie Benner and Michael S. Schmidt contributed reporting.