The Republican chairman of the House Oversight Committee has demanded that the FBI hands over all documents it has relating to the communications between President Donald Trump and the bureau's former director, James Comey.

Chairman Jason Chaffetz sent the letter a few hours after The New York Times first reported that Trump allegedly asked Comey to end the FBI's investigation into former National Security Adviser Michael Flynn.

Flynn resigned in February following reports that he misled Vice President Mike Pence about his conversations with Russia's ambassador to the US, Sergey Kislyak.

In an interview with NBC News, Chaffetz said that if the memo exists and accurately recorded the conversation, "that seems like an extraordinary use of influence to try to shut down an investigation being done by the FBI".

Chaffetz tweeted later: "I have my subpoena pen ready."

Senator John McCain suggested that the growing scandal was starting to match the size of Watergate.

House Speaker Paul Ryan appeared to endorse Chaffetz. "We need to have all the facts, and it is appropriate for the House Oversight Committee to request this memo," said AshLee Strong, a spokeswoman for Ryan.

Chaffetz will also have the support of Democratic members of his committee.