Sacked FBI director James Comey has agreed to testify before the Senate intelligence committee at a public hearing.

Comey was fired by President Donald Trump last week amid an agency probe into alleged Russian meddling in the US election.

The committee said in a statement the hearing would be scheduled after the May 29 Memorial Day holiday.

The committee's chairman, Senator Richard Burr, and the ranking Democrat, Senator Mark Warner, announced on Friday (local time) that Comey will testify in an open setting before the committee.

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The date of the hearing has not yet been set.

Burr says the committee wants to hear from Comey on his role in the development of the US intelligence agencies' assessment that Russia interfered in last year's election.

He says he hopes Comey's testimony will answer some of the questions that have arisen since Comey's sudden dismissal.

It comes amid revelations Mr Trump reportedly bragged to Russia that he had fired 'nut job' FBI boss James Comey and that it would ease pressure on him.

President Donald Trump told Russian officials in the Oval Office that James Comey was a "crazy nut job" and firing him had relieved "great pressure".

Mr Trump reportedly told Russian Foreign Minister Sergey Lavrov and Russian Ambassador Sergey Kislyak: "I just fired the head of the FBI. He was crazy, a real nut job. I faced great pressure because of Russia. That's taken off. I'm not under investigation."

The comments were reported by the New York Times and taken from a White House document summarising the meeting.

Sean Spicer, the White House press secretary, did not dispute the account.

Mr Trump met with the Russian diplomats on May 10, the day after he fired Mr Comey.

Mr Comey had been investigating whether there was collusion between Russia and anyone connected to the Trump campaign during last year's election.

US President Donald Trump meets with Russian Foreign Minister Sergey Lavrov, left, next to Russian Ambassador to the US Sergei Kislyak at the White House. Photo / AP
US President Donald Trump meets with Russian Foreign Minister Sergey Lavrov, left, next to Russian Ambassador to the US Sergei Kislyak at the White House. Photo / AP

In a statement Mr Spicer said Mr Comey's pursuit of the probe had harmed Mr Trump's ability to deal with Russia over issues including Syria and Ukraine.

Mr Spicer said: "By grandstanding and politicising the investigation into Russia's actions James Comey created unnecessary pressure on our ability to engage and negotiate with Russia."

It emerged earlier this week that at the same Oval Office meeting Mr Trump shared with the Russian diplomats classified intelligence relating to a plot by ISIS.

The intelligence had come from Israel, which had not agreed for it to be shared. Israel later stood by Mr Trump who said he had an "absolute right" to share it.

Democrats have argued that Mr Trump's firing of Mr Comey during his Russia investigation could amount to obstruction of justice.

A special counsel, Robert Mueller, has now been appointed to investigate Russian meddling in the election.

'Current White House official is significant person of interest in Russia investigation'

It came as a current White House official was identified as a "significant person of interest" in the investigation into any coordination between the Trump campaign and Russia, the Washington Post reported.

The person was said to be a White House adviser "close to the president", officials told the newspaper. They also said that did not mean any criminal charges were near.

President Donald Trump. Photo / AP
President Donald Trump. Photo / AP

Trump departs for first overseas tour

The latest controversy came as Mr Trump set out for the Middle East on his first trip abroad as president.

Saudi Arabia rolled out the red carpet as Mr Trump embarked on a charm offensive to gain support for his plans to forge an "Arab Nato".

The president will be served his favourite meal of steak and ketchup when he sits down for dinner tonight as his hosts try to accommodate the US leader.

In Riyadh, where Mr Trump's repeated denunciations of Iran have been welcomed, US flags lined roads along with pictures of Mr Trump and King Salman and the message "Together we prevail".

President Donald Trump and first lady Melania Trump wave as they board Air Force One at Andrews Air Force Base. Photo / AP
President Donald Trump and first lady Melania Trump wave as they board Air Force One at Andrews Air Force Base. Photo / AP

The trip is set to be a crucial test of Mr Trump's ability to rally allies and assert himself on the world stage, and a chance to leave behind the domestic turmoil that has engulfed his White House.

Saudi Arabia is the first of five stops on a marathon nine-day world tour and Mr Trump is expected to unveil a major arms deal, brokered by his son-in-law Jared Kushner, worth more than $100 billion over a decade.

Aides said he would also discuss his vision for an "Arab Nato" including Saudi Arabia, the United Arab Emirates, Egypt and Jordan aimed at fighting terrorism and countering Iran.

Saudi Arabia invited leaders and representatives of 55 countries for the visit. Perhaps the highlight was due to be a speech by Mr Trump on Islam, drafted by his adviser Stephen Miller. Mr Miller played a key role in drawing up the president's travel ban aimed at barring people from a group of predominantly Muslim countries entering America.

The White House said Mr Trump would use the speech to emphasise the "need to confront radical ideology".

US allies expressed concern at Mr Trump's rhetoric during last year's election campaign about withdrawing America from its commitments around the world.

Hours before setting out from Washington, Mr Trump said: "Getting ready for my big foreign trip. Will be strongly protecting American interests - that's what I like to do!"

But aides said his message would be one of "unity to America's friends".

In an ambitious trip Mr Trump will go on to Israel, Rome, Brussels for a Nato meeting, and Sicily for the G7.

- additional reporting by news.com.au