WASHINGTON — President Trump asked the F.B.I. director, James B. Comey, to shut down the federal investigation into Mr. Trump’s former national security adviser, Michael T. Flynn, in an Oval Office meeting in February, according to a memo Mr. Comey wrote shortly after the meeting.

“I hope you can let this go,” the president told Mr. Comey, according to the memo.

The documentation of Mr. Trump’s request is the clearest evidence that the president has tried to directly influence the Justice Department and F.B.I. investigation into links between Mr. Trump’s associates and Russia. Late Tuesday, Representative Jason Chaffetz, the Republican chairman of the House Oversight Committee, demanded that the F.B.I. turn over all “memoranda, notes, summaries and recordings” of discussions between Mr. Trump and Mr. Comey.

Such documents, Mr. Chaffetz wrote, would “raise questions as to whether the president attempted to influence or impede” the F.B.I.

Mr. Comey wrote the memo detailing his conversation with the president immediately after the meeting, which took place the day after Mr. Flynn resigned, according to two people who read the memo. It was part of a paper trail Mr. Comey created documenting what he perceived as the president’s improper efforts to influence a continuing investigation. An F.B.I. agent’s contemporaneous notes are widely held up in court as credible evidence of conversations.

Mr. Comey shared the existence of the memo with senior F.B.I. officials and close associates. The New York Times has not viewed a copy of the memo, which is unclassified, but one of Mr. Comey’s associates read parts of it to a Times reporter.

“I hope you can see your way clear to letting this go, to letting Flynn go,” Mr. Trump told Mr. Comey, according to the memo. “He is a good guy. I hope you can let this go.”