Michael Flynn's request for immunity from prosecution in exchange for testifying to the Senate commission investigating alleged ties between members of Trump's circle and Russia has been rejected.

Flynn, who resigned as President Donald Trump's national security adviser, was told the move was "wildly preliminary" and "not on the table" at this point, a senior congressional official told NBC.

However this does not rule out immunity being granted at a later date, as the investigation is ongoing.

Flynn also offered to speak to the Justice Department in exchange for immunity from prosecution, according to NBC.

Flynn, the former director of the Defense Intelligence Agency, resigned from his role as a national security adviser in February, after it was revealed he had held meeting with Russian ambassador Sergei Kislyak and discussed sanctions ahead of Trump's election.

The White House claims Flynn did not inform Vice President Mick Pence about the meetings, and Pence subsequently defended Flynn in a television interview.

In a statement Thursday, Flynn's lawyer Robert Kelner said no "reasonable person" would get questioned in "such a highly politicised, witch-hunt environment without assurance against unfair prosecution."

Trump defended Flynn's request for immunity. "Mike Flynn should ask for immunity in that this is a witch hunt (excuse for big election loss), by media & Dems, of historic proportion!" Trump wrote in a tweet.

Congressional committees and the FBI are also investigating allegations that Russia interfered in the 2016 presidential election in a bid to help secure Trump's victory.

Senator Angus King, a member of the Senate Intelligence Committee, has said of Trump's remarks on Flynn "This is not a witch hunt... This is an effort to get to the truth of some very important questions.

"There is no doubt whatsoever that the Russians were behind an effort to interfere in our elections," he told CNN. "To continue to deny that - it just flies in the face of all of the reality."