President Trump asked the FBI 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.

After writing up a memo that outlined the meeting, Mr. Comey shared it with senior F.B.I. officials. Mr. Comey and his aides perceived Mr. Trump’s comments as an effort to influence the investigation, but they decided that they would try to keep the conversation secret even from the F.B.I. agents working on the Russia investigation so the details of the conversation would not affect the investigation.

The Jan. 27 dinner came a day after White House officials learned that Mr. Flynn had been interviewed by F.B.I. agents about his phone calls with the Russian ambassador, Sergey I. Kislyak. On Jan. 26, the acting attorney general, Sally Q. Yates, told the White House counsel about the interview, and said Mr. Flynn could be subject to blackmail by the Russians because they knew he had lied about the content of the calls.