New Zealand Prime Minister Jacinda Ardern has gone into labour and checked into an Auckland hospital for the birth of her first child.

Deputy Prime Minister Winston Peters has been made New Zealand’s Acting Prime Minister and will run the country for the next six weeks while Ms Ardern takes maternity leave, the PM’s office said in a statement Thursday morning.

It said Ms Ardern, 37, arrived at Auckland City Hospital at 5:05am local time (3.05am AEST).

Ms Ardern took office as New Zealand’s third female prime minister last year and in January announced she was expecting a baby with her partner, TV fishing show presenter Clarke Gayford, 40.

The New Zealand PM will be just the second world leader to give birth while in office, after Pakistan’s then-prime minister Benazir Bhutto 28 years ago.

News of the imminent birth comes after Ms Ardern was snapped by Mr Gayford on Wednesday mulling over paperwork on her Auckland couch, three days after her the baby was due.

Mr Gayford, posted the snap on Twitter, with the hashtag “#stillwaiting”.

He warned any aspiring PMs: “Make sure you also have an appetite for reading and reading and reading and reading.”

Anyone with aspirations of being PM, make sure you also have an appetite for reading and reading and reading and reading. #stillwaiting pic.twitter.com/AzwzkYPIKD

— Clarke Gayford (@NZClarke) June 20, 2018

Ms Ardern, who had been patiently playing the maternity waiting game by running the country from home, had said she was willing to be induced – “Yep, out” – if her pregnancy went too far past her June 17 due date.

On June 16, she told NZ media outlet Newshub she had “sort of” packed her bag and was “pretty much” ready to go when the baby was.

“Everything that anyone would think to take – toothbrush, pyjamas, not much more than that,” she said.

“I’ve always heard that you can really overdo it with those bags. I’ve kept mine pretty simple, pretty basic.”

One thing tougher than the packing was deciding on a name for the baby, Ms Ardern said in late May.

“We’ve got a list. It’s not getting any shorter and it has no favourites, so it’s not going well,” she said.

“It’s one of those things where Clarke’s absolutely convinced it will come to us as soon as it arrives. I think we’ll be sleep-deprived and probably angry at each other, so I don’t think that’s the best time to choose.”

When it came to the labour itself, “I’ve been very careful not to buy into this sense of overdramatisation,” Ms Ardern told Newshub.

She said she thought the baby’s arrival would be fast: “Things happen pretty slowly. Well, in some cases. I think I’ll be one of those.”

When the couple leave hospital with their newborn, they will pose briefly for photos and questions from media.

They have asked for privacy after that, “in the weeks set aside to be together after the birth, and during private family moments”.

-with AAP