Jacinda Ardern's feeling overwhelmed by the public support, following the birth of her first child.

The 3.31-kilo baby girl arrived at 4.45 yesterday afternoon.

Finance Minister and friend of the Prime Minister, Grant Robertson, spoke to her shortly after the birth.

He told Mike Hosking she and partner Clarke Gayford still can't quite believe it.

"She is incredibly happy at that moment all new parents have in welcoming a beautiful new girl into the world. Her and Clarke are just thrilled and grateful for all of the support they have received."

LISTEN ABOVE AS FINANCE MINISTER GRANT ROBERTSON SPEAKS TO MIKE HOSKING