The explosive new development on Tuesday followed a week of tumult at the White House after Trump fired Comey and then discussed sensitive national security information about Islamic State with Russian Foreign Minister Sergei Lavrov.
The Comey memo, first reported by the New York Times, is likely to raise questions about whether Trump tried to interfere with a federal investigation.
Comey wrote the memo after he met in the Oval Office with Trump, the day after the president fired Flynn on February 14 for misleading Vice President Mike Pence about the extent of his conversations last year with Russia's ambassador, Sergei Kislyak.
“I hope you can let this go,” Trump told Comey, according to a source familiar with the contents of the memo.
The New York Times said that during the Oval Office meeting, Trump condemned a series of government leaks to the news media and said the FBI director should consider prosecuting reporters for publishing classified information.
The White House denied the report in a statement, saying it was "not a truthful or accurate portrayal of the conversation between the President and Mr. Comey."
Flynn's resignation came hours after it was reported that the Justice Department had warned the White House weeks earlier that Flynn could be vulnerable to blackmail for contacts with Kislyak before Trump took office on January 20.
Kislyak was with Lavrov at the White House last week when Trump disclosed the sensitive information.
A spokeswoman for the FBI declined to comment on the details of the memo.
The new development came as Republican and Democratic lawmakers pressured Trump to give a fuller explanation for why he revealed sensitive intelligence information to Lavrov.
The information had been supplied by a US ally in the fight against the Islamic State militant group, the officials said.
Potential FBI chiefs steer clear
The Trump administration's search for a new FBI Director hit roadblocks on Tuesday, after two high-profile potential candidates, a moderate judge and a conservative senator, indicated they do not want the job.
Advisers to Judge Merrick Garland and US Senator John Cornyn, of Texas, told Reuters they discouraged them from leading the Federal Bureau of Investigation, cautioning that they would be leaving important, secure jobs for one fraught with politics and controversy.
The advisers, who spoke on the condition of anonymity, said the new FBI director would have little job security and heightened scrutiny by political observers following Trump's abrupt firing of Comey on May 9.
Garland and Cornyn have distanced themselves from the selection process just three days before Trump has said he may make a decision. This points to the difficulties the White House has in filling the FBI post amid turmoil in the administration.
Trump's firing of Comey, the man in charge of an investigation into possible collusion between 2016 election campaign associates and the Russian government, has outraged many lawmakers, including some Republicans.
Garland, the chief judge of the US Court of Appeals for the District of Columbia Circuit, "loves his job and is not interested in leaving the judiciary," said one source familiar with the judge's thinking.
Cornyn said in a statement that he had informed the White House that "the best way I can serve is continuing to fight for a conservative agenda in the US Senate."
White House spokesman Sean Spicer told reporters on Tuesday that an announcement on FBI director was still possible before Trump leaves on his first foreign trip on Friday. He said the US Department of Justice was still interviewing candidates.
