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.