“I hope you can see your way clear to letting this go, to letting Flynn go,” the president told Comey, according to the Times.
An associate of Comey’s who has seen the memo told Reuters that the details of the document as reported by the Times were accurate.
An unnamed source also told CNN Comey was “so appalled by the request that he wanted to document it.”
The White House quickly responded, saying it never asked Comey or anyone else to end the investigation into Flynn.
The news comes as Trump is embroiled in a debate about allegedly leaking classified information to Russia’s foreign minister.
Flynn was asked to resign after less than a month on the job — and just days before the meeting outlined in Comey’s memo. The White House said he misled Vice-President Mike Pence and other top officials about his communications with Russia’s ambassador to the United States.
Comey, who was overseeing the probe into the Trump campaign’s ties to Russia, was fired by the president a week ago.
Reasons for his termination were varied: first the president said it was done on the recommendation of the deputy attorney general, but then he took credit for the decision himself, saying he believed “the Russia thing” was a made-up story.
Despite Trump’s plea to the ex-FBI director, the probe into Flynn’s ties to Russia continued.
Comey shared the memo with other FBI officials, the Times said, since Comey “perceived Mr. Trump’s comments as an effort to influence the investigation.” But it was ultimately decided that knowledge of the meeting could influence the investigation itself.
Democratic Rep. Adam Schiff, who sits on the Senate Intelligence Committee looking into Russian ties, says today’s allegations are “among the most disturbing to date.” He said Comey will likely come back to testify in the investigation.
He also said he would like to see Comey’s notes on the subject, as well as any recorded tapes Trump may have on their meetings.
In a letter to the current FBI director Andrew McMcabe, Rep. Jason Chaffetz of the committee on oversight and government reform, directed the FBI to hand over Comey’s memo and any other memoranda “referring or relating to any communications between Comey and the President,” by May 24, 2017.
“If true, these memoranda raise questions as to whether the President attempoted to influence or impede the FBI’s investigation as it relates to Lt. Gen. Flynn,” the letter, obtained by NBC News, reads.
WATCH: U.S. senators react to New York Times claims that Trump asked Comey to halt Flynn investigation
*with a file from the Associate Press
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