Laurell Ardern, who has spoken to her daughter since the birth, said the new parents were feeling comfortable and happy with how things had turned out.
It's been revealed the baby was wearing a hat knitted by a supporter, and a baby shawl knitted by Clarke Gayford's mum, in the photo that went around the world yesterday.
Deputy Prime Minister Winston Peters has stepped in as acting prime minister and will run the country for the next six weeks while Ardern takes maternity leave, according to an agreement they published earlier.
The items included clothing, a muslin wrap, a merino blanket and a piece of pounamu, she said. A spokeswoman for the prime minister said Thursday that Gayford had driven Ardern to the hospital in the couple's own vehicle.
The family are planning to stay there for another night at least.
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Ardern has reportedly just woken up after a brief sleep and a dinner of Marmite toast and milo last night.
"We're a family that are fairly well grounded and to see this on the global media is absolutely different - I can say that without a shadow of a doubt", Ross Ardern told RNZ. "So, I'm dying to see it and hold her and just see what's she's like". "Thank you", Ardern said. He was part of the support team "as all members of our family will be".
New Zealand has long had a progressive reputation and was the first country to give women the right to vote in 1893 and Ardern is the country's third female prime minister.
"A wee girl evens up the numbers on our side as I have three boys and our sister has two girls", she said.
New Zealand leader Jacinda Ardern will spend a second night in hospital with her "very alert and hungry" newborn daughter who Twitter wags have dubbed the "prime miniature".
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"I'm so excited to be an Aunty and can't wait to have cuddles".
"The nurses described the baby as "very alert and one hungry baby", the spokesman added.
Helen Clark, one of two other women who have been New Zealand's prime minister, said Thursday in an email that the nation had taken Ardern's pregnancy in stride.
"People are really interested in this first family and the statements they are making about gender equality and choice, Clark told Newstalk ZB".
The public has generally been supportive of the popular prime minister.
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We are also a close group and I think that takes us a long way. "We know they're a physical team". It's more around the flow of the day, leave maximum time for physical recovery.
Ross Ardern said he thought Mr Gayford would make a "great" stay-at-home dad. "It's a story for men and women, this story; a very human story".