“I’m talking to him; we’ve had a good talk,” said the president.

Rosenstein’s job security has been a subject of near-constant speculation almost since the moment he got it in early 2017. But it seemed never more at risk than after a New York Times story last week said the No. 2 official at the Justice Department had once suggested secretly recording the president and mustering support to use the 25th Amendment of the constitution to remove him from office.

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“My preference would be to keep him and to let him finish up,” Trump said. “He said he never said it. He said he doesn’t believe it. He said he has a lot of respect for me.”

A departure by Rosenstein could spark fresh fights within different parts of the government, as he is overseeing special counsel Robert S. Mueller III’s investigation into Russian interference in the 2016 campaign and whether any Trump associates conspired with those efforts.

Trump and Rosenstein had planned to meet Thursday afternoon to discuss the matter, but the president suggested Wednesday that meeting may not happen and that he wasn’t particularly concerned about the issue.

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“I may call Rod tonight or tomorrow and ask for a little bit of a delay to the meeting,” Trump said, adding that he wanted to focus tomorrow on the Senate hearing over embattled Supreme Court nominee Brett M. Kavanaugh.

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The latest chapter in the ongoing saga of Rosenstein’s tenure may be the most confusing, as just days ago senior Justice Department officials had become convinced that he was about to quit or be fired.

Rosenstein has frequently been the target of attacks from a president furious over the Russia investigation, but behind the scenes, the relationship between the two men is often amiable, according to people familiar with their talks and meetings.

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In recent administrations, it was unusual for a president and the No. 2 Justice Department official to interact much. But a chain of events that began in the early days of the Trump presidency has thrust the two of them closer — a strange relationship that has somehow survived the frequent turbulence of the administration.

Traditionally, the job of deputy attorney general is one that draws intermittent political fire from congressional leaders or internal Justice Department critics but rarely rises to the level of national political debate. Rosenstein, however, has operated in the job under the harsh glare of national politics as he tries to navigate the hypercharged politics of the Russia investigation.

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At times, Rosenstein has been attacked by Democrats; more recently, the president’s congressional allies have tried to force him out of the job.

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James M. Trusty, a former Justice Department official now at the Ifrah Law firm who is close to Rosenstein, said the deputy attorney general’s constantly shifting position in the eyes of each political party is probably due to his own lack of interest in politics.

“During Rod’s tenure, he’s obviously drawn fire from both sides of the aisle at various junctures, and at the heart of the political problem is that he’s not a politician,” Trusty said. “He just keeps his head down and prosecutes cases or investigates cases. Ultimately, in a town like Washington, that’s maddening to everyone.”

Part of the reason for Trump and Rosenstein’s frequent interactions lies in how Rosenstein came to supervise the Russia investigation. Attorney General Jeff Sessions, who as a senator was one of Trump’s earliest backers during the GOP primaries, infuriated the president by recusing himself in early 2017 from the investigation into Russian election interference.

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Advisers to the president said he has never forgiven Sessions for that decision, so much so that Trump dislikes talking to — or even about — the attorney general.

That has meant that the president interacts often with the very person overseeing the investigation into his conduct.

“Based on my observations, Rod enjoys working with the president and respects him and what he is trying to accomplish,” said Ian Prior, a former Justice Department spokesman. “As a longtime prosecutor, I think Rod truly enjoys being in leadership at the Justice Department in an administration with a law-and-order president that supports law enforcement.” On issues of crime, the opioid crisis and illegal immigration, Prior said, “they are on the same page.”

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Earlier this week, it appeared a final break was imminent. Rosenstein publicly disputed the assertions about what he had said in those May 2017 discussions but privately told senior White House officials that he was willing to resign in the wake of the revelations, as long as the president would commit to not publicly disparaging him once he left the job, according to people familiar with the conversations.

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Those conversations, from Friday to Sunday evening, led White House and Justice Department officials to think Rosenstein would soon be out.

They were wrong.

White House officials now say they expect Rosenstein to stay in the job until after the election, when both he and Sessions are likely to be replaced.

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When the president first nominated Rosenstein for the job, he was serving as the U.S. attorney in Baltimore, having held that job in both Republican and Democratic administrations. The pick was seen as uncontroversial and was met with relief by many Justice Department veterans, who felt Rosenstein would bring a degree of stability and institutional perspective to the table.

Shortly after assuming the job, Rosenstein made a fateful decision — writing a memo sharply critical of then-FBI Director James B. Comey’s handling of the investigation of Hillary Clinton’s use of private email when she was secretary of state. That memo was used to justify Comey’s firing, but days later the president said in a television interview that he was thinking about the Russia case when he decided to fire Comey.

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Publicly, the Rosenstein memo made him an instant villain of the left — someone who had seemingly caved to political pressure to help the president weaken an investigation of those close to him. Even within the Justice Department, some officials privately questioned Rosenstein’s decision and worried he had been manipulated. Days later, Rosenstein appointed Mueller as special prosecutor, which tempered much of the criticism he had received at that point from Democrats.

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