US President Donald Trump has said he will move quickly to nominate a new FBI director, after he sparked a political firestorm by firing the man investigating possible collusion between Russia and the Trump presidential campaign.

Mr Trump told reporters he might even be able to make his decision on who should succeed James Comey to lead the Federal Bureau of Investigation before he leaves on his first foreign trip on Friday.

"Even that is possible," Mr Trump said, speaking on Air Force One before departing for Lynchburg, Virginia, where he delivered a commencement address.

"I think the process is going to go quickly," he said, adding that the candidates under consideration were mostly well known.

"They've been vetted over their lifetime essentially. But very well known, highly respected, really talented people. And that's what we want for the FBI."

Critics have assailed Mr Trump for abruptly dismissing Mr Comey, who was leading the agency's investigation into alleged Russian meddling in the 2016 US election, and possible ties between Moscow and the Trump presidential campaign.

Russia denies the claims and the White House says there was no collusion.

Mr Trump made the remarks to reporters prior to speaking to about 50,000 people at Liberty University in Lynchburg, where he did not mention Mr Comey or the controversy his dismissal on Tuesday caused.

It was Mr Trump's first public event outside the White House since Mr Comey's ousting.

A White House official has said 11 people are under consideration to replace Mr Comey as FBI chief, a position that requires confirmation by the Republican-led US Senate.

Acting FBI Director Andrew McCabe, Republican Senator John Cornyn, New York Appeals Court Judge Michael Garcia and former Assistant Attorney General Alice Fisher were scheduled to be interviewed today, an administration official said.

In addition, FBI special agent Adam Lee and US District Judge Henry Hudson were expected to be interviewed, the Washington Post reported.

The FBI Agents Association, which claims more than 13,000 active and retired agents as its members, has endorsed another candidate: former Representative Mike Rogers, who had also worked as an FBI agent.

At Liberty, the US's largest Christian college, Mr Trump peppered his remarks with the kind of anti-establishment rhetoric that fuelled his maverick presidential campaign, telling graduates to challenge "entrenched interests."

He thanked the crowd for their support and repeatedly invoked his own unlikely election victory.

"Relish the opportunity to be an outsider," Mr Trump said. "The more that a broken system tells you that you're wrong, the more certain you should be that you must keep pushing ahead."

He also had strong words that seemed aimed at his critics.

"No one has ever achieved anything significant without a chorus of critics standing on the sidelines explaining why it can't be done," Mr Trump said.

"Nothing is easier or more pathetic than being a critic, because they're people that can't get the job done."