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The name of the baby, born on Thursday, is yet to be released.
Media have just been briefed on the latest information about the baby, her mother and father Clarke Gayford.
The baby slept well last night but Ardern did not fare so well, media were told.
The baby will be given her first bath this afternoon and a new photo of her is expected to be released today.
Media have been camped out at a room at Auckland Hospital since the PM arrived in labour early on Thursday morning.
Moments ago reporters were told the PM had porridge for breakfast and had opted to stay in hospital for a third night.
Usually, new mums leave hospital soon after delivering and go to Birthcare in Parnell to recover.
Because of the security arrangements needed by the Prime Minister and Gayford, she has had to stay at the hospital. Ardern's mother Laurell is said to be en route to Auckland to meet her new granddaughter, but her flight was delayed.