US President Donald Trump has characterised the leak of former FBI director James Comey's memo of their conversations "cowardly" and suggested the act could have legal consequences.

Comey admitted Thursday in testimony before the Senate intelligence committee that, after Trump fired him on May 9, he asked a friend to leak his documentation of a meeting with the president to the press in the hope of prompting the appointment of a special prosecutor to investigate Russian election interference.

Comey said he felt it was necessary to take notes on his meetings and conversations with Trump because he feared the president would lie about what took place.

"I believe the James Comey leaks will be far more prevalent than anyone ever thought possible. Totally illegal? Very 'cowardly!'" Trump said on Twitter.

I believe the James Comey leaks will be far more prevalent than anyone ever thought possible. Totally illegal? Very 'cowardly!'

— Donald J. Trump (@realDonaldTrump) June 11, 2017

The leaks created a political firestorm over whether Trump pressured Comey to drop an investigation into contacts between Russian officials and Michael Flynn, who briefly served as Trump's national security advisor.

US correspondent Richard Arnold told Mike Hosking Trump rejects those allegations.

"Comey testified last week that the President, in a private conversation with Comey, asked the FBI boss to let go the agency's investigation into Mike Flynn, Trump's ousted national security adviser."

Comey said he believed Trump fired him because of the Russia investigation, and Trump himself cited "this Russia thing" as a motivating factor for his decision to sack Comey during an interview with broadcaster NBC that aired last month.

Opposition Democrats have said that the leaks occurred after Comey was fired and no longer a government official.

LISTEN ABOVE: US CORRESPONDENT RICHARD ARNOLD SPEAKS WITH MIKE HOSKING