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New Zealand Prime Minister Jacinda Ardern has apologised for insulting a political rival in parliament.

The offensive comment was picked up by microphones following a question by David Seymour, leader of the opposition ACT party.

Mr Seymour objected to the remark and asked the House of Representatives Speaker to have it withdrawn.

Ms Ardern - whose party has fallen behind in polls in the past 12 months - later said she had apologised.

In a lively debate on Tuesday, the prime minister took issue when Mr Seymour asked her to give an example of her "making a mistake, apologising for it properly, and fixing it".

Ms Ardern said there had been a number of occasions where her Labour administration had acknowledged there had not been "perfect responses", including a key element of the country's Covid response.

"We have openly said, for instance, that [managed isolation and quarantine] was something that was very difficult at the time and that there were people that were affected by it and that we would do things differently if we were ever confronted with it again."

She added that she stood by the work of her government over its term in office.

"We've always made decisions that we believe to be in the best interest of New Zealand at the time," she said.

After sitting down, Ms Ardern could be heard quietly saying: "Such an arrogant prick."

A spokesperson from the prime minister's office confirmed that Ms Ardern had since apologised to Mr Seymour.

The prime minister received international praise for her strict response to the Covid pandemic, and has enjoyed high approval ratings for much of her two terms in office.

But with New Zealand expected to go to the polls in late 2023, Ms Ardern is coming under increasing political pressure.

Latest opinion polls have the Labour Party trailing opposition party National by around five percentage points.