They say everyone is in "good spirits" and that baby is "very cute".
Ms Ardern said she and her partner had opted for the alternative spelling Neve rather than the traditional Niamh, to avoid confusion.
The first family spent three nights at Auckland City Hospital adjusting to parenthood since the baby was born at 4.45pm on Thursday.
At almost three days old the tiny tot will make her first public appearance at 11am cradled in mother Jacinda Ardern's arms with proud dad Clarke Gayford.
Ardern is one of only a few female leaders to give birth while holding office - the most recent being former Pakistani PM Benazir Bhutto, who had her daughter in 1990.
"To me, in those moments, we just saw a reflection of how open and generous New Zealanders are".
Speaking to media from the town of Nelson, Ardern's parents Ross and Laurell Ardern said the baby had been very active during the night and had kept their daughter awake.
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Laurell Ardern said she'd had people come up to her saying that her daughter had been an inspiration, including one woman who anxious a job was too hard for her, but then thought 'Well, if Jacinda can do it, I will do it'.
When Deswal discovered she had the same due date as Ardern - June 17 - she realised there would be a chance the two would cross paths in hospital. "Sleep deprived, but super well", she said.
Ardern, 37, became New Zealand's youngest prime minister when she took office through a coalition deal past year after an inconclusive election.
"We chose Neve because we just liked it", she told reporters. Ardern, on the other hand, has had a public pregnancy, delegated duties to a deputy, and will take a reasonable six weeks of maternity leave.
New Zealand Prime Minister Jacinda Ardern said she was blown away by well-wishes from around the world. "So, I'm dying to see it and hold her and just see what's she's like".
Support also flooded in from around the world, with Britain's Queen Elizabeth, whom Ardern met in London in April, sending an emailed message of congratulations and Canadian Prime Minister Justin Trudeau tweeting at Ardern: "Pro tip, Jacinda: Briefing notes make excellent bed time stories".
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".