New Zealand Prime Minister Jacinda Ardern is raising money for a prostate cancer charity by auctioning off a transcript of a parliamentary exchange in which she called a political opponent an "arrogant prick."

Bidding for a framed copy of the document, signed by Ardern and the insult's target, political rival David Seymour, had reached NZ$45,500 (US$29,000) by Friday in an online auction.

New Zealand's premier was overheard muttering the insult following a heated exchange between the pair at a parliamentary session on Tuesday.

A microphone picked up an exasperated Ardern saying "he's such an arrogant prick" in reference to Seymour as she retook her seat after answering a barbed question from the MP.

Seymour, leader of the right-liberalist ACT party, petitioned the speaker of New Zealand's parliament for an apology by Ardern, which meant her comment was entered into the official record, known as the Hansard.

Ardern later texted an apology to Seymour, who came up with the idea of joining forces to raise money for charity.

"We are thrilled it's got such good support," Seymour told AFP Friday, with bidding due to close on December 22.

In a Facebook post on Thursday, Ardern said she had signed the official transcript with Seymour "in the spirit of good sportsmanship and a good cause."

Seymour said the prime minister needed little persuasion.

"I suggested we sign a copy of the Hansard and auction it off to raise money for the foundation and pricks everywhere," he added.

Seymour said her insult "was not significant in terms of the stuff that goes on, people were surprised as it's so out of character" for Ardern.

He added he hoped the signed document would go "for a lot of money. It's a pretty unusual occurrence and a good cause."