NZ prime minister Jacinda Ardern reveals new baby Neve

New Zealand's prime minister has named her baby daughter Neve Te Aroha Ardern Gayford, as she and partner Clarke Gayford left hospital.

Ms Ardern said the couple had struggled for months to decide on a name but had decided to wait until their baby was born to see which one suited her.

She said Neve meant bright, radiant and snow.

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

"Te Aroha was our way of reflecting the amount of love this baby has been shown even before she even arrived... it's also the place where all my family are from and I grew up under that mountain."

Aroha means "love" in Maori, while Mt Te Aroha is a 952-metre mountain in the Kaimai Range, on New Zealand's North Island.

The "Ardern" would serve as another middle name, meaning the baby is known as "Neve Gayford", she added.

Mr Gayford said that the birth had been "all a bit of a blur... for both of us", but added: "I won't forget the look on Jacinda's face when she finally held the baby... she looked absolutely just stunned and very, very happy."

Little Neve was born on Thursday afternoon New Zealand time, weighing 7.3lb, but the prime minister was kept in hospital for three days mainly due to security arrangements.

On Sunday, the little baby made her first public appearance at Auckland City Hospital, appearing to sleep soundly as her parents answered a few questions for waiting reporters.

Ms Ardern, who described herself as doing well but being "sleep-deprived", plans to take six weeks off work before Mr Gayford takes on the bulk of the parenting duties.

The 37-year-old, who is only the second elected world leader to give birth while in office, said her partner was "being as much of a role model as I am".

She added: "I hope for little girls and boys that 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. Simple."

The baby was welcomed with congratulatory messages from world leaders and royals, including from the Queen and the Duke and Duchess of Sussex, something Ms Ardern described as "mindblowing". The royal couple will visit New Zealand as part of a tour later this year.

Other gifts included a bouquet of flowers form the Saudi Embassy that was so large that it would not fit into the room and was moved to the ward to be shared with other new mothers.

But Ms Ardern added that she also treasured the messages from "those people who took time to send a little note, or a blanket, or a set of booties".

Mr Gayford, known in New Zealand as the "first bloke", is the presenter of a fishing show, and Ms Ardern was the youngest New Zealand PM in 150 years, but she said they would not put pressure on their new baby.

"We're not placing any great expectations on this baby - except happiness and love," she said.