US President Donald Trump asked then FBI Director James Comey to end the agency's investigation into ties between former White House national security adviser Michael Flynn and Russia, according to a source who has seen a memo written by Comey.

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 of Iraq and the Levant (ISIL) with Russian Foreign Minister Sergey Lavrov.

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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, Sergey Kislyak.

"I hope you can let this go," Trump told Comey, according to a source familiar with the contents of the memo.

The White House denied the report. "The president has never asked Mr Comey or anyone else to end any investigation, including any investigation involving General Flynn," it said in a statement.

Al Jazeera's Mike Hanna, reporting from Washington, DC, noted the significance of the information being written down in a memorandum, which would be admissible in a court of law.

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"This is a very serious matter indeed. Why this is so serious - if indeed it is proved to be true - is that this is a clearly illegal act - attempting to halt or obstruct an FBI investigation," said Hanna.

"What we are going to see in the coming days from the House and the Senate is growing momentum for James Comey to clarify whether or not President Trump actively attempted to interfere with the investigation into Michael Flynn. This could have massive ramifications."

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 added it was "not a truthful or accurate portrayal of the conversation between the President and Mr Comey".