The FBI was reeling after President Donald Trump unexpectedly fired its director James Comey, with agency staff scheduling an emergency high-level meeting for Tuesday night amid speculation about who would replace Comey in the top job.

An FBI official, who was not authorised to speak to reporters and so asked not to be identified, said the staff meeting would explore next steps for the law-enforcement agency.

Trump sacked Comey amidst a probe into the Trump 2016 presidential campaign's possible collusion with Russia to influence the election outcome, sparking backlash from some Democrats in Congress who said the decision had the appearance of a cover-up and some Republicans who called the timing troubling.

The official said the FBI had no idea the Trump administration was considering dismissing Comey and the news "took even top officials by surprise".

An FBI spokesman did not respond to a request for comment.

Deputy Director Andrew McCabe was expected to step in for now, but he was unlikely to be nominated by Trump for the director's post, said two former FBI officials.

Comey, who was appointed by former Democratic President Barack Obama, had 6-1/2 years left in his term as director of an agency with 56 US field offices and more than 30,000 employees.

The new director must be appointed by Trump and confirmed by the US Senate.

Comey is the third high-profile law-enforcement official to be fired under Trump. Preet Bharara was fired as US attorney for the Southern District of New York and Sally Yates was fired as acting attorney general.

Trump, a Republican businessman and former TV celebrity, was elected on 8 November and took office on 20 January.

One possible contender for director of the Federal Bureau of Investigation is Dana Boente, No 3 at the Justice Department and former acting attorney general, said the two former FBI officials.

Other potential choices include Republican Representative Trey Gowdy, a former prosecutor who led a congressional inquiry into former secretary of state and 2016 Democratic presidential nominee Hillary Clinton's role in the 2012 attacks on the U.S. Consulate in Benghazi, Libya.

Close campaign allies of Trump include former New York Mayor Rudy Giuliani and Milwaukee County, Wisconsin, Sheriff David Clarke. But both men would be seen as highly political nominees for an agency designed to be independent.

"The White House has to avoid all the politicos if they are going to get a nominee through the Senate," said one of the former FBI officials.

Boente was tapped to temporarily lead the Justice Department's Trump-Russia investigation after Attorney General Jeff Sessions, a Trump appointee, stepped down because of his dealings with Russian Ambassador Sergei Kislyak.

Rod Rosenstein replaced Boente in that role when the Senate confirmed him as deputy attorney general last month. Rosenstein served as a federal prosecutor under both Republican President George W Bush and Obama.

A lengthy memo from Rosenstein on Tuesday faulted Comey for his handling of an FBI probe of Clinton's private email server.