The meeting that nearly led to Mr. Session’s resignation came last May shortly after the president fired James B. Comey, the F.B.I. director who was heading an investigation into Russia’s interference in the 2016 presidential election and any cooperation with Mr. Trump’s campaign. The dismissal of Mr. Comey, which Mr. Trump in an interview with NBC News linked to his unhappiness with the Russia investigation, triggered the appointment of a special counsel, Robert S. Mueller III, to the ire of the president.

Mr. Trump was furious with Mr. Sessions for recusing himself from the Russia investigation and therefore losing control over it. Mr. Priebus’s account confirms and adds more detail to a New York Times report that the president berated Mr. Sessions in a meeting in the Oval Office, leading him to offer his resignation. Vice President Mike Pence and the White House counsel, Donald F. McGahn II, were in the meeting, but Mr. Priebus was not.

“Don McGahn came in my…

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