An FBI investigation into possible links between Donald Trump's campaign and alleged Russian interference in the 2016 US presidential election continues despite the sacking of director James Comey, the bureau's acting chief has said.

"There has been no effort to impede our investigation to date," Andrew McCabe told the Senate Intelligence Committee on Thursday, two days after Comey's dismissal by Trump, in a move that sent shockwaves across Washington.

"You cannot stop the men and women of the FBI from doing the right thing," McCabe added.

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Contradicting President Trump's claims that Comey had lost the support of rank and file members of the bureau, McCabe told the panel that the axed director was held in the highest regard at the FBI.

"I can tell you also that Director Comey enjoyed broad support within the FBI and still does to this day," McCabe said

"I have the highest respect for his considerable abilities and his integrity," McCabe added. "And it has been the greatest privilege and honour of my professional life to work with him."

'FBI in turmoil'

His comments came as Trump labelled Comey a "showboat" and a "grandstander" in an interview with NBC, revealing that he was planning to fire him regardless of the recommendation from the justice department.

"The FBI has been in turmoil," Trump told NBC News in his first interview since firing Comey. "I was going to fire Comey. My decision," Trump said.

Trump told NBC he had previously asked Comey whether he was under investigation in the Russia matter, speaking with Comey once over dinner and twice by telephone.

"I said, 'If it's possible, would you let me know, am I under investigation?'" Trump told NBC. "He said, 'You are not under investigation.'"

Comey has neither publicly discussed conversations with Trump, nor has he publicly commented on his dismissal.

McCabe testified it was not typical practice to tell a person they are not a target of an investigation.

At the daily White House briefing, spokeswoman Sarah Huckabee Sanders was asked whether it was a conflict of interest for a president to ask the FBI chief such a question. She answered: "No, I don't believe it is."

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On Wednesday night, the Senate panel ramped up its months-long investigation by issuing subpoenas for documents related to Russia from Michael Flynn, Trump's former national security adviser.

Flynn was fired by Trump only three weeks into the job for misrepresenting to Vice President Mike Pence the nature of conversations he had in December with the Russian ambassador to Washington.

He had previously refused the committee's requests to submit the documents voluntarily.

The committee has asked Comey to testify before the panel in private next Tuesday, according to the panel's senior Democrat, Mark Warner.