PM, partner introduce their baby

New Zealand Prime Minister Jacinda Ardern and her partner Clarke Gayford with baby Neve.

Ms Ardern and her partner, television fishing personality Clarke Gayford, welcomed a baby girl weighing 3.3kg on Thursday afternoon.

A radiant Ms Ardern revealed her daughter's name is Neve Te Aroha Ardern-Gayford.

Neve Te Aroha Ardern Gayford with her parents, Jacinda Ardern and Clarke Gayford.

She told Sky News: "We had been told that it was unlikely that we would be able to have a family without help".

The couple had settled on the baby's first name, Neve, after she was born, Ardern said, explaining that it means "bright and radiant" and "snow", which reflected that she was born in the middle of winter during the nation's indigenous Maori new year and the shortest day of the year.

"I thought 'how do I reflect the generosity, particularly of all the iwi who gifted us names?' and Te Aroha seemed to be a way".

"It was all a bit of a blur for the both of us but she had obviously been through so much and finally the moment had arrived, and she looked absolutely stunned and very, very happy".

She went on to thank everyone at Auckland City Hospital for the "kindness, warmth, and care" they had shown the family throughout their stay.

"It was pretty special", she added.

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Gayford said he would never forget the look on Ardern's face when she held their baby.

"So I hope for little girls and boys that actually there's a future where they can make choices about how they raise their family and what kind of career they have that are based on what they want and what makes them happy", she said.

Ardern announced she was pregnant back in January, just months after she'd taken office as the country's third female prime minister.

The couple with their newborn daughter on Thursday.

Ardern said she "feels very lucky" and thanked everyone for their best wishes after the birth, as she updated her social media accounts from the comfort of her hospital bed.

"From the midwives, to the nurses, even the people we saw less of - the security team who have been with us, the comms team here at the hospital, the people who came and cleaned our room and gave us food".

"We wanted to say thank you (to New Zealanders for their support) and we are all doing really well".

"Over the next six weeks we'll do what every other parent does and learn the little nuisances ... and just figure things out as we go".

Ardern, 37, became New Zealand's youngest prime minister when she took office through a coalition deal previous year after an inconclusive election.

She said she hoped in time those sorts of choices would be more accepted.