WELLINGTON, New Zealand — New Zealand’s prime minister, Jacinda Ardern, said she had named her first child Neve Te Aroha Ardern Gayford, as she left an Auckland hospital with her partner on Sunday, three days after her daughter was born.

Ms. Ardern, the leader of the center-left Labour Party and the first sitting world leader to give birth in almost three decades, will take six weeks of parental leave before returning to work.

The deputy prime minister, Winston Peters, who is the leader of a minor party, is acting prime minister in her absence.

At a short news conference on Sunday, Ms. Ardern, 37, who had said before the birth that she and her partner, Clarke Gayford, were struggling to name their child, said they had chosen Neve for a first name because “we just liked it.”