New Zealand Prime Minister Jacinda Ardern has left hospital with her baby daughter.

Ms Ardern left Auckland City Hospital this morning with partner Clarke Gayford by her side.

Her tiny daughter was wrapped in a cosy blanket and wearing a green knitted beanie to keep her warm.

The NZ PM told reporters of her joy, thanking the public for their support.

“We’re not placing any great expectations on this little baby except for happiness and love,” she said.

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

Ms Ardern said she and her partner had opted for the alternative spelling Neve rather than the traditional Niamh, to avoid confusion.

The Irish name means “radiant” or “bright”.

“We’ve gone for simplicity, because Clarke with an ‘e’ has caused all sorts of problems, and Jacinda with a ‘d’,” she said.

Ms Ardern said like most new parents, she and Mr Gayford “went through the struggle” of choosing a name for a matter of months

“We chose Neve because we just liked it, and when we met her she just looked like she suited the name,” she said.

The name also means “snow”, which Ms Ardern said seemed like a “good combination” for Matariki, the Maori New Year, and the winter solstice, which was when her daughter born.

“Te Aroha”, the name of a rural town on New Zealand’s North Island, was chosen to reflect Ms Ardern’s family history.

The couple joked that they were feeling well but “sleep-deprived”.

Mr Gayford said the birth was “all a bit of a blur for both of us”, but he “won’t forget the look on Jacinda’s face when she arrived”.

In a cute touch, Ms Ardern thanked New Zealanders for their gifts, especially the hand-knitted ones.

“Those moments have mattered as much to us as any of those lovely messages of support from around the world,” she said.

All the presents for baby Neve would be passed on to another family once they had been used, Ms Ardern said.

The 37-year-old is the first world leader to give birth in office since the late Benazir Bhutto of Pakistan in 1990.

Ms Ardern will be the first world leader to take maternity leave. She will take six weeks of parental leave before returning to work, at which point Mr Gayford, the host of a television show about fishing, will become a stay-at-home parent.

The couple welcomed baby Neve, who weighed 3.31 kgs (7.3lbs), on June 21 at New Zealand’s largest public hospital.

She posted a photo to her Instagram account, saying: “Welcome to our village wee one.

Feeling very lucky to have a healthy baby girl that arrived at 4.45pm weighing 3.31kg (7.3lb) Thank you so much for your best wishes and your kindness. We’re all doing really well thanks to the wonderful team at Auckland City Hospital.”

Gayford tweeted the same photo of the happy couple and their newborn baby on Twitter, saying: “So happy to announce our little girl has finally arrived! Everyone healthy and happy.

7.3lb, 4.45pm. Huge thanks to all involved, what a team.”

The PM’s pregnancy announcement prompted a national conversation in NZ about working mothers.