"I hope you can see your way clear to letting this go, to letting Flynn go", Trump told Comey, according to the article.
A small number of FBI agents were made aware of the memo and the conversation, and agents kept working on the investigation.
The panel portion of "Special Report" usually runs during the final 25 minutes of the program, but was featured for the full hour to discuss the breaking news around the Comey memo. "He is a good guy. I hope you can let this go".
Trump added that Flynn had done nothing wrong.
Comey did not say anything to Trump about curtailing the investigation, only replying: "I agree he is a good guy".
The White House disputed a report Monday that President Donald Trump asked former FBI Director James Comey to shut down an investigation into ousted national security adviser Michael Flynn.
"The president has the utmost respect for our law enforcement agencies, and all investigations", continues the statement.
In testimony to the Senate last week, the acting FBI director, Andrew McCabe, said, "There has been no effort to impede our investigation to date".
The FBI declined to comment Tuesday.
Some Republicans also called for action, asking Comey to speak to Congress and demanding that any memos or recordings of his conversations with the president be presented to them.
Trump wrote to Comey that the dismissal was necessary to restore public trust and confidence.
"He documents everything", one source said.
The meeting in question took place February 14, the day after Trump fired Flynn because he had misled colleagues - including Vice President Pence - about the substance of phone calls he had with the Russian ambassador to the United States, Sergey Kislyak.
Comey had been in the Oval Office that day with other senior national security officials for a terrorism threat briefing.
Schumer said in a brief, somber floor speech Tuesday that he was "shaken" by the report that Trump asked Comey "to shut down an active investigation into a close political associate". The newspaper cites a memo Comey wrote following the meeting.
October 28, 2016: Days before the election, Comey informs Congress by letter that he is reopening the investigation into Clinton's email practices based on new evidence, citing the discovery of emails on a laptop used by a top Clinton aide.
Rep. Jason Chaffetz, R-Utah, who leads the powerful House Oversight and Government Reform Committee, sent a letter to acting Federal Bureau of Investigation director Andrew McCabe, asking for all notes, summaries, or recordings of communications involving Trump and Comey, by May 24. At that dinner, on January 27, Trump asked Comey at least two times for a pledge of loyalty, which Comey declined, according to one of Comey's associates.
Comey's friends immediately started leaking to reporters that the former top cop was "not anxious about any tapes" of talks between him and the president.
After the meeting, Comey's associates did not believe there was any way to corroborate Trump's statements.
The turmoil overshadowed Republican legislative priorities such as healthcare and tax reform and laid bare sharp divisions between the White House and USA intelligence agencies, which concluded late a year ago that Russian Federation had tried to influence the 2016 presidential election in Trump's favor. That resignation, however, came almost three weeks after former acting attorney general Sally Yates warned the Trump administration that Mr Flynn might be compromised by Russians.