Andrew McCabe, the former FBI deputy director who was fired on Friday, kept detailed notes about his interactions with President Donald Trump, according to US media.

McCabe has said he believed his firing was because he corroborated former FBI Director James Comey's claim that Trump tried to pressure him into killing a probe into Russian interference in the 2016 US election.

Comey has told Congress he kept a detailed written record of his conversations with Trump.

Special Counsel Robert Mueller is leading the probe into possible collusion between Trump campaign officials and Russia during the presidential election, a claim that Trump has denied.

Trump on Saturday criticised the FBI as he hailed the firing of McCabe as a "great day for democracy".

Critics described the axing of McCabe as a "dangerous" ploy to discredit the top US law enforcement agency as well as the work of Mueller, as McCabe is a potential key witness in the Russia probe.

Trump on Saturday via Twitter blasted the alleged "tremendous leaking, lying and corruption at the highest levels of the FBI, Justice & State".

He also reiterated long-running criticism of the Mueller investigation, terming it a "witch-hunt" and saying that it "should never have been started in that there was no collusion and there was no crime".

McCabe job offer

Earlier, Trump's personal lawyer, John Dowd, told the Daily Beast that he hoped Deputy Attorney General Rod Rosenstein would follow the lead of the FBI Office of Professional Responsibility and "bring an end to alleged Russia Collusion investigation manufactured by McCabe's boss James Comey based upon a fraudulent and corrupt Dossier".

Dowd told the Daily Beast he was speaking for the president. But in a subsequent statement, he said he had been "speaking for myself, not the president".

McCabe, who has endured a year of withering attacks from Trump, was fired by the Justice Department late on Friday, just two days before he was to retire after 21 years with the FBI.

Critics say the firing is a step in Trump's plan to engineer Mueller's dismissal, potentially sparking a constitutional crisis.

Mueller is also examining whether Trump might have obstructed justice, including by firing Comey last May.

One Democratic lawmaker, Mark Pocan of Wisconsin, announced on Saturday that he offered McCabe a job in his office so he can complete the time necessary to retire with full federal benefits.

"My offer of employment to Mr McCabe is a legitimate offer to work on election security," Pocan said in a statement.

McCabe spokeswoman Melissa Schwartz was non-committal. "We are considering all options," she told the Washington Post.