US President Donald Trump told Russian officials at the White House that firing FBI Director James Comey relieved "great pressure" the president was facing from an ongoing probe into Russia and the US presidential election, the New York Times reported today, citing a document summarising the meeting.

"I just fired the head of the FBI. He was crazy, a real nut job," Mr Trump said, according to the Times, which cited a document read to it by a US official. "I faced great pressure because of Russia. That’s taken off."

The Times said the document was based on notes taken from inside the Oval Office. Reuters was not immediately able to verify the accuracy of the Times' account.

Mr Trump left for Saudi Arabia today on the first leg of a trip that the White House hopes will shift attention away from the political firestorm triggered by his firing last week of Mr Comey.

The trip, which also includes stops in Israel, Italy and Belgium next week, has been billed by the administration as a chance to visit places sacred to three of the world's major religions while giving Mr Trump time to meet with Arab, Israeli and European leaders.

But uproar in Washington threatened to cast a long shadow, after Mr Comey's firing, allegations Mr Trump had previously pressed the FBI chief to stop investigating former national security adviser Michael Flynn, and the subsequent appointment of a special counsel to look into alleged Russian meddling in the 2016 election and possible ties to Mr Trump's campaign.

Mr Trump, who has embraced what he describes as an "America First" approach to US foreign policy and international trade, is expected to be welcomed warmly by leaders in Saudi Arabia and Israel.

Lingering questions over his views on the Iran nuclear deal, commitment to NATO security and scepticism of the Paris climate agreement, however, could generate tension at meetings with European counterparts in Brussels and Sicily.

"It's almost always true that when a president goes on a big foreign trip, especially one that has some important summits ... that that dominates the news and knocks most other stuff out," said Republican strategist Charlie Black.

"Whether by accident or design, this will help him in terms of Russia news for a while."

Mr Trump, who has expressed a desire for friendlier relations with Moscow, drew a storm of criticism this week when it emerged that he had shared sensitive national security information with Russia's foreign minister during a meeting last week in the White House.

The president was already under attack for firing Mr Comey in the midst of an FBI probe into Russia's role in the 2016 election and possible collusion with Mr Trump campaign members. Moscow has denied any such interference. Mr Trump has denied collusion and denounced the appointment of a special counsel as a witch hunt.

His fellow Republicans in Congress have expressed frustration that Mr Trump's pro-business economic agenda, highlighted by a plan to cut corporate and individual taxes, have been pushed to the backburner by the turmoil.

"He clearly did have a bad two weeks. And clearly it's my hope that he does ... right the ship, that he improves so that we can just get going," Republican House Speaker Paul Ryan said on the Hugh Hewitt radio show today.