The No. 2 Democrat in the Senate, Richard Durbin, slammed the president after Friday's tweets, telling MSNBC that the president is "dangerous because he may be obstructing justice in terms of the investigation. and secondly his credibility has been destroyed".
The BBC's Laura Bicker in Washington says Mr Trump was referring to a private White House dinner in January during which the president claims Mr Comey assured him he was not being investigated over alleged links to Russian Federation.
"I think the process is going to move quickly because nearly all of them are very well-known, they've been vetted over their lifetime essentially", he said. Asked whether Rogers or Cornyn would be good choices, Graham flatly said, "no".
They are among almost a dozen candidates Trump is considering, a group that includes several lawmakers, attorneys and law enforcement officials.
Schiff said. "If there are tapes, of course, that would be the best evidence of what took place".
US President Donald Trump is "assaulting" the country's institutions, according to a former director of national intelligence.
Comey's firing ignited a firestorm in Washington and has prompted speculation over whether Trump's decision hinged on his apparent anger at the FBI's probe into the Trump campaign's potential collusion with Russian Federation during the 2016 election.
There are several other candidates reportedly on Trump's short list to replace Comey, whom he abruptly fired on Tuesday. Under rules of the Senate, Republicans could still confirm an Federal Bureau of Investigation director with 51 votes.More news: National Hockey League playoffs: Energized Ducks beat Predators, even Western finals
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When the opposite occurred, Trump grew incensed - both at Democrats and his own communications staff for not quickly lining up more Republicans to defend him on television.
So far 14 people - lawmakers, attorneys and law enforcement officials among them - have emerged as candidates.
Alice Fisher, a high-ranking Justice Department official in former President George W. Bush's administration, was among those scheduled to be interviewed Saturday.
In the initial moments after Comey's firing, Trump's press secretary, deputy press secretary and Vice President Mike Pence all said Trump's decision was based on the recommendation of Deputy Attorney General Rod Rosenstein.
However, sources have told Fox News that at least one additional candidate is being interviewed Saturday - Adam Lee, the special agent in charge at the FBI's Richmond office.
Andrew McCabe was the FBI's deputy director until the abrupt departure of his boss.
The Federal Bureau of Investigation probe and parallel congressional investigations have cast a cloud over Trump's presidency since he took office on January 20, threatening to overwhelm his policy priorities.