In a statement, the White House denied the version of events in the memo saying Mr Trump has never asked Mr Comey or anyone else to end any investigation, including any investigation involving General Flynn. As president, he has stressed the illegality of leaking classified information and suggested that those who do so should be punished. Yet U.S. allies and some members of Congress expressed concern bordering on alarm.
"This is not a truthful or accurate portrayal of the conversation between the President and Mr Comey".
Leaders of the congressional investigations into Russian meddling into the USA election a year ago are also calling on Comey to testify.
Some Democratic lawmakers and former intelligence officials warned that, depending on what exactly Trump told Russian Foreign Minister Sergei Lavrov and Ambassador Sergey Kislyak, the lives of those gathering the intel provided by Israel to the US may now be at risk.
Despite the conversation between Trump and Comey, the investigation of Flynn has proceeded.
Mitch McConnell, the Republican leader of the Senate, said simply: "It would be helpful to have less drama emanating from the White House". The New York Times has not viewed a copy of the memo, which is unclassified, but one of Comey's associates read parts of the memo to a Times reporter.
Flynn resigned the day before the February 14 meeting, after it was revealed he apparently had lied to his about the nature of his contacts with Russia's ambassador.
The intensifying drama comes as Trump is set to embark Friday on his first foreign trip, which had been optimistically viewed by some aides as an opportunity to reset an administration floundering under an inexperienced president.
Trump abruptly fired Comey last week, in a move Democratic lawmakers decried as an attempt to short-circuit the Russian Federation investigation. But the White House has provided differing accounts of the firing.
Trump was apparently referring to the FBI's ongoing counterintelligence inquiry into possible collusion between Trump campaign associates - including Flynn - and Russian officials seeking to influence the presidential election.
Sen. Mark Warner of Virginia, the top Democrat on the Senate Intelligence Committee, said he will ask Comey for additional material as part of the panel's investigation.
McCain says Trump needs to "get it all out. and the longer you delay, the longer it's going to last".
Comey's retelling of the meeting has Trump telling him: 'I hope you can see your way clear to letting this go, to letting Flynn go'.
"As President I wanted to share with Russian Federation (at an openly scheduled W.H. meeting) which I have the absolute right to do, facts pertaining to terrorism and airline flight safety", Trump said on Twitter.
The newspaper said Comey was in the Oval Office that day with other national security officials for a terrorism threat briefing.
According to the Times, Comey wrote in the memo that Trump told him Flynn had done nothing wrong.
Trump wrote to Comey that the dismissal was necessary to restore public trust and confidence. National Security Adviser H.R. McMaster said the president's comments were "wholly appropriate". That information reportedly involved longstanding Islamic State group plans to bring down a civilian aircraft using a bomb concealed inside a laptop.
"He documents everything", one source said.
The Justice Department declined to comment.
Two U.S. officials said Trump shared the intelligence, supplied by a U.S. ally in the fight against the militant group, with Russian Foreign Minister Sergei Lavrov and Russian Ambassador Sergei Kislyak during a meeting last Wednesday.
"It's textbook", the source said.
Associated Press writers Vivian Salama and Jill Colvin contributed.