New Zealand Prime Minister Jacinda Ardern has apologised after a hot microphone caught her calling an opposition MP an “arrogant p—k” in parliament.

Ms Ardern uttered the insult after responding to a barrage of questions from right-wing ACT party leader David Seymour on Tuesday.

After answering questions on inflation, immigration and her under-fire Foreign Minister Nanaia Mahuta, Ms Ardern took her seat and quietly said “such an arrogant p—k”.

Deputy Prime Minister Grant Robertson is heard replying “he is” to the insult, which was picked up and broadcast.

Ms Ardern’s office confirmed she sent an apology to Mr Seymour, who addressed journalists after question time.

“Jacinda Ardern texted me and said ‘I apologise. It’s not something I should have said’,” Mr Seymour said.

“She said ‘as my mum would say, if you don’t have anything nice to say don’t say it’. I agree with the sentiment.

“I just said ‘thank you and I hope you have a very merry Christmas’ … it’s water off a duck’s back.”

The outburst is a departure from Ms Ardern’s self-described “relentlessly positive” brand of politics, coming on the second last parliamentary day of the year.

Mr Seymour sought to make political mileage out of the insult, saying “the apology we’re really looking for is from New Zealanders worried about rising prices and ram raids”.

“I think she’s under a lot of pressure because her policies aren’t working,” he said.

Ironically, the last question in Mr Seymour’s train of attacks was “can the Prime Minister give an example of her making a mistake, apologising for it properly and fixing it?”

Mr Seymour’s ACT, a right-wing and socially progressive party, is the fourth-largest in New Zealand, with 10 MPs in Wellington.

Polls put ACT on track to form government with the centre-right National party after next year’s election.

National leader Chris Luxon, who will be prime minister if polls hold, also issued an apology on Tuesday.

In a conversation about what turns young people to a life of crime, Mr Luxon said gang life might look attractive to young people in South Auckland, a region with a high Maori and Pacific population.

“If you’re sitting in a garage in South Auckland with your two brothers and you’re thinking about life and where you’re going, consciously or unconsciously, the gang life looks pretty attractive,” he said.

The response drew pushback from many in the community.

Ms Ardern accused Mr Luxon of “stereotyping an entire generation”.

The 52-year-old said he didn’t resile from the comments but he “wasn’t meaning to disrespect South Auckland”.

“We have to have some courage in this country if we’re going to talk about challenges about crime … if people were offended I’m sorry about that,” he said.

“I’m not apologising for having serious, substantive conversations about what causes crime.”

-AAP