US President Donald Trump’s defence lawyer Alan Dershowitz has said his argument against impeaching the president was “distorted”.

The former Harvard Law professor complained on Thursday about the portrayal of his testimony at Mr Trump’s Senate trial that a president, if he believes his re-election is in the “national interest,” is essentially immune from impeachment for actions in support of that idea.

That argument left even some of the president’s top allies backing away from the claim.

“They characterised my argument as if I had said that if a president believes that his re-election was in the national interest, he can do anything,” the retired professor said on Thursday.

“I said nothing like that, as anyone who actually heard what I said can attest.”

Mr Dershowitz testified to Senate jurors late on Wednesday that the quid pro quo charge at the heart of Trump’s impeachment – a trade of US military aid for political favours – even if proven could not be grounds for his impeachment.

“Every public official that I know believes that his election is in the public interest,” he said on Wednesday night.

“And if a president does something, which he believes will help him get elected in the public interest, that cannot be the kind of quid pro quo that results in impeachment.”

That argument was an abrupt turnaround from Mr Trump’s own claim of “perfect” dealings with Ukraine.

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John Bolton’s revelations have been countered by the president’s lawyers (Patrick Semansky/AP)

Meanwhile, Democrats are pressing hard to force the Senate to call more witnesses to testify but Republicans appear intently focused on bringing the impeachment trial to a vote of acquittal, possibly in a matter of days.

New revelations from former national security adviser John Bolton are being countered by the president’s lawyers, who used Wednesday’s unusual question-and-answer session to warn off prolonging the proceeding.

Democrats argued Mr Bolton’s forthcoming book cannot be ignored.

It contends he personally heard Mr Trump say he wanted military aid withheld from Ukraine until it agreed to investigate Joe Biden and his son, Hunter Biden.

The abuse of power charge that is the first article of impeachment. Mr Trump denies saying such a thing.

The vote on calling witnesses is expected by Friday.

At one point Wednesday night, as Chief Justice John Roberts fielded queries, Texas Republican Ted Cruz asked if it mattered whether there was a quid pro quo.

Simply, no, declared Mr Dershowitz, who said politicians often equate their reelection with the public good.

“That’s why it’s so dangerous to try to psychoanalyse a president,” he said.

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House impeachment manager Adam Schiff answers a question during the impeachment trial (Senate Television/AP)

Adam Schiff, the Democrat leading the House prosecutors, appeared stunned.

“All quid pro quos are not the same,” he retorted.

“Some might be acceptable some not. And you don’t need to be a mind reader to figure out which is which. For one thing, you can ask John Bolton.”

With voting on witnesses later this week, Democrats, amid the backdrop of protesters swarming the Capitol, are making a last-ditch push to sway Republicans to call Mr Bolton and others to appear for testimony and ensure a “fair trial”.

Mr Trump faces charges from the House that he abused his power like no other president, jeopardising Ukraine and US-Ukraine relations by using the military aid as leverage while the vulnerable ally battled Russia.

The second article of impeachment says Trump then obstructed the House probe in a way that threatened the nation’s three-branch system of checks and balances.