National is urging the prime minister to support a vote of no confidence in the speaker, after obtaining a statement of claim in the defamation case of the man Trevor Mallard wrongly accused of being a rapist.
The claim alleges Mallard's lawyer said they would "vigorously" defend any defamation claim, despite Mallard already knowing he was wrong.
Mallard settled the case in December and in a statement apologised for the "distress and humiliation" his incorrect comments had caused.
He then told a parliamentary committee he knew "probably within 24 hours" he had made a mistake.
The remarks were made on RNZ in May 2019, after the release of a report which revealed frequent bullying and harassment at Parliament.
The statement of claim, seen by RNZ, alleges in the hours following those comments, Mallard had communications with Parliamentary Service chief executive Rafael Gonzales-Montero.
"From this time, if not before, the defendant was aware that the complaint was not, and did not concern, an allegation of rape," the statement claimed.
However, Mallard stood by his comments when asked about them by media that afternoon.
National has twice tried - and failed - to move a motion of no confidence in Mallard as speaker.
Shadow leader of the House Chris Bishop said it was "very concerning" that Mallard would "knowingly make a false claim about someone".
What was more troubling, he said, was the statement of claim alleged that a month after Mallard made the comments, his lawyers wrote to the plaintiff's lawyers, saying they did not accept he had been defamed and would "defend any claim vigorously".
The statement alleges the lawyers "threatened" that if the plaintiff pursued the case "the question of his reputation and his conduct will be very much the centrepiece of any public proceedings".
Bishop said this showed that Mallard was not fit to be speaker.
"What Mr Mallard essentially did was behave in a threatening and bullying way towards this parliamentary employee, that who, in his own words, he knew within 24 hours he had falsely accused.
"He fought the case for 18 months. He said that if the case went to trial he would prove truth. He said that if the case went to trial he would put the plaintiff's own reputation on trial.
"That is behaviour totally unbecoming of a person who is meant to uphold the standards and the integrity of Parliament," Bishop said.
He said Jacinda Ardern needed to support National's motion of no confidence in Mallard.
"She needs to ask herself if this is the behaviour she is willing to stand behind. In any other workplace in New Zealand Mr Mallard would be sacked. And what is good for any other workplace should be good for Parliament as well.
"They say that it's the sort of behaviour that you walk past that you're prepared to accept. Is Jacinda Ardern prepared to tolerate this sort of behaviour, is she prepared to walk past it?," he said.
RNZ has approached the office of the speaker for comment.
Ardern said the statement of claim did not raise any issues that had not already been traversed.
"He has rightly acknowledged the errors that have been made, apologised and of course the proceedings have been settled.
"In my view, though, the information that's been brought to the table here is in substance no different to what's already been at select committee," she said.
Ardern said she did not think that Mallard should be removed as speaker, and she rejected accusations that he is a bully.
"Not in my view. But in this case he has done wrong and he has apologised for that," she said.