Prime Minister Jacinda Ardern and partner Clarke Gayford pictured with their new arrival last night.

Prime Minister Jacinda Ardern's first night as a mum was similar to other new mothers - sleepless.

Ardern and her partner Clarke Gayford were due to make a public appearance today, but have cancelled so that they can rest up.

A statement from the Prime Minister's office said both parents were "really well, if not a bit tired".

"In fact, the PM has just woken after what sounded like a pretty brief sleep," a spokesperson said.

"She tells us nurses have described the baby as 'very alert and one hungry baby'." 

The Prime Minister's daughter was born at 4.45pm at Auckland City Hospital and weighs 3.31kg.

The baby was one of 24 born yesterday at Auckland hospital.

 - Stuff