In remarks to the media in the Oval Office on Tuesday, Mr. Trump said he was not troubled that Mr. Sessions met with the special counsel and he denied a report that Mr. Wray had threatened to resign.
“He didn’t at all,” Mr. Trump said of Mr. Wray, adding: “He did not even a little bit. Nope. He’s going to do a good job.”
The report, by the website Axios, said Mr. Sessions was pressuring Mr. Wray, at the president’s behest, to clear the F.B.I. of loyalists to Mr. Comey. But Mr. Wray responded that he needed to move at his own pace to make changes, and that if Mr. Sessions and the president wanted replacements made more quickly, someone else would have to do it, a person familiar with the exchange said, adding that Mr. Wray stopped short of threatening to quit.
Mr. Wray’s tenure has been tense as the president has repeatedly fanned suspicion about whether the F.B.I.’s work is politically motivated, including the Russia investigation.
Mr. Trump and his allies have focused their ire on Andrew G. McCabe, the bureau’s deputy director. Mr. McCabe’s wife was a Virginia State Senate candidate in 2015, and she received donations from the “super PAC” supporting the state’s governor at the time, Terry McAuliffe, a longtime ally of Hillary Clinton’s.
One person familiar with Mr. McCabe’s meetings with the president said there had been a small handful of encounters between the two the week Mr. Comey was fired, as Mr. Trump was deciding whether to name Mr. McCabe the acting director.
At one of the meetings, another person said that Mr. Trump asked Mr. McCabe who he had voted for in the 2016 presidential election. Mr. McCabe said he had not voted. The meeting was first reported by The Washington Post.
At their final meeting, Mr. Trump offered him the job and told him he planned to give him the role of acting director, and that the president planned to make a rally-the-troops appearance at the F.B.I. Headquarters that week. Mr. McCabe responded that it would be a risky move for the president to show up at the building after firing a well-respected director, so Mr. Trump scuttled the trip, citing scheduling conflicts.
Though Mr. Wray has resisted the pressure to change Mr. McCabe’s role, he has begun to alter the F.B.I.’s leadership. He removed James Baker, the general counsel for the bureau under Mr. Comey, and replaced him with Dana Boente, the United States attorney for the Eastern District of Virginia and the acting head of the Justice Department’s national security division, according to a person familiar with the move.
Mr. Wray also said in a statement on Tuesday that he has replaced his departing chief of staff, James Rybicki, who served under Mr. Comey, with Zachary Harmon, whom Mr. Wray worked with in private practice and who previously served at the Justice Department.
During the daily White House news briefing, the press secretary, Sarah Huckabee Sanders, insisted that the president has “100 percent” confidence in Mr. Wray and that it was up to Mr. Wray to decide how to handle the bureau’s leadership.
A Justice Department spokeswoman, Sarah Isgur Flores, confirmed that the interview with Mr. Sessions occurred. He was accompanied to the interview by the longtime Washington lawyer Chuck Cooper.
For Mr. Mueller, Mr. Sessions is a key witness to two of the major issues he is investigating: the Trump campaign’s possible ties to the Russians and whether the Mr. Trump tried to obstruct the Russia investigation.
Mr. Mueller can question Mr. Sessions about his role as the head of the campaign’s foreign policy team. Mr. Sessions was involved in developing Mr. Trump’s position toward Russia and he met with Russian officials, including the ambassador.
Along with Mr. Trump, Mr. Sessions led a March 2016 meeting where one of the campaign’s foreign policy advisers, George Papadopoulos, pitched the idea of a personal meeting between Mr. Trump and President Vladimir V. Putin of Russia. Mr. Papadopoulos pleaded guilty in October to lying to federal authorities about the nature of his contacts with Russians and agreed to cooperate with the special counsel’s inquiry.
When Mr. Trump learned in March that Mr. Sessions, by then the attorney general, was considering whether to recuse himself from overseeing the Russia investigation, the president had the White House’s top lawyer, Donald F. McGahn II, lobby Mr. Sessions to remain in charge of the inquiry.
Mr. Sessions instead followed the guidance of career prosecutors at the Justice Department, who advised him that he should stay out of the investigation. When Mr. Trump was informed, the president erupted in anger, saying he needed an attorney general to protect him.
The special counsel’s investigators have also asked witnesses about the president’s desires to fire Mr. Sessions, whom Mr. Trump has criticized publicly and privately for recusing himself from the inquiry, though he has left Mr. Sessions in charge of the Justice Department.
Mr. Trump believes Mr. Mueller would never have been appointed if Mr. Sessions had not stepped aside. After Mr. Mueller was appointed in May, Mr. Trump again grew angry at Mr. Sessions, who offered to resign. Days later, Mr. Trump rejected that offer.
The questions that Mr. Mueller’s investigators have asked in relation to Mr. Comey were based in part on information he provided during his own interviews with the special counsel’s office last year, according to people familiar with the matter. In one of his memos, Mr. Comey wrote that Mr. Trump had asked him to end the F.B.I.’s investigation into Mr. Flynn.
After the president’s request was revealed publicly, the deputy attorney general, Rod J. Rosenstein, appointed Mr. Mueller as the special counsel to lead the Russia investigation and examine whether the president obstructed justice.