Prime Minister Jacinda Ardern will be spending a third night in hospital.
Ms Ardern and her partner Clarke Gayford are expected to speak to the media from the ninth floor of the hospital about their baby shortly before leaving on Sunday morning, at 11am.
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Afterwards there will be no more interaction with media while the couple take the next six weeks to bond with her baby in private.
Once the six weeks is over Ms Ardern will return to her role as Prime Minister and Mr Gayford will become a stay-at-home dad.
On Saturday, the baby's grandmother said it was "unbelievable" to hold the newborn for the first time.
"She's such a little cutie and with such fine features."
Laurell Ardern said she thought the baby looked more like her father.
She had not given her daughter any advice.
"Jacinda works things out for herself."
Ms Ardern and Mr Gayford have received well wishes and presents from all over the world.
Japanese Prime Minister Shinzo Abe and the Commonwealth Secretariat have passed on notes of congratulations, while the Saudi Embassy sent a bouquet of flowers so large it does not fit in Ms Ardern's room.
She has put them in the maternity ward reception.
Newshub.
