The Times report cites a memo written by Comey, which appears to provide evidence Trump tried to influence the FBI's investigation into links between Russian Federation and Trump's campaign.
Comey, who was sacked by Trump last week, detailed his conversation with the president in the memo immediately after the meeting, said the report.
On Tuesday, the New York Times reported Trump asked Comey to shut down an investigation into Flynn.
"This is not a truthful or accurate portrayal of the conversation between the president and Mr. Comey", the statement said.
"I hope you can see your way clear to letting this go, to letting Flynn go", Trump told Comey, according to the memo. The then-FBI chief shared the existence of such memos with senior staff and his close aides at the agency.
Comey, according to the Times' sources, was uncomfortable with the exchange and documented it in a contemporaneous memo that he shared with just a few senior Federal Bureau of Investigation and Department of Justice officials.
Putin slammed critics who spread allegations about Trump's ties with Russian Federation. However, a former USA government official told Fox News, "That's not how it works".
Republicans must join Democrats in insisting that the president cooperate with Mueller's investigation and the two inquiries led by the House and Senate intelligence committees. "It is obvious there are some people out there that want to harm the president", Ryan told reporters at a news conference.
In his resignation letter, Mr Flynn said he held numerous calls with the Russian ambassador during the transition and gave "incomplete information" about those discussions to Vice-President Mike Pence. Comey had previously declined to testify in front of the Senate Intelligence Committee, but some media reports indicated that he would likely comply with the new requests.
The documents have to be delivered by May 24, Efe news said. While the president does have authority to disclose classified information, there's concern that it may have damaged national security.
"The country is being tested in unprecedented ways".
"The memo is powerful evidence of obstruction of justice and certainly merits immediate and prompt investigation by an independent special prosecutor", said Democratic US Senator Richard Blumenthal. "The president must be impeached", said Green who is the first member of Congress to officially request leveling charges against the president.
Striking a defiant stance, he added: "You can't let the critics and the naysayers get in the way of your dreams".