The town Prime Minister Jacinda Ardern's daughter Neve was named after has commemorated her birth by gifting the family a print of the mountain, a voucher for the local hot pools and a jar of jam.

Matamata-Piako District Council celebrated the birth of Neve Te Aroha Ardern Gayford who was born on Thursday June 21 at 4.45pm with a shared morning tea at the council and some Te Aroha-themed gifts for the family.

A council spokeswoman confirmed the council gifted Jacinda Ardern and partner Clarke Gayford with a photo of Te Aroha mountain, taken by its own graphic designer Grace Bonnar, Mayor Jan Barne's favourite homemade jam from Pippins in Matamata, a Te Aroha Mineral Spa voucher for the family and a few small Te Aroha branded gifts.

The jam is a popular choice with Barne's who often purchases a jar from the local florist to take with her when visiting residents.

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Arden previously told media they had chosen Te Aroha as a middle name to reflect the "love and generosity" shown to the baby.

"It's also the place where all my family are from and I grew up under that mountain," Ardern said at the time.

Ardern is currently taking six weeks maternity leave before handing the reins to Gayford who will be a stay-at-home dad.

The family has largely stayed out of the public eye since leaving Auckland City Hospital when Neve was just three days old. The only exception has been earlier this month when Arden posted a live video from her couch while cradling Neve to celebrate the launch of the $1.5 billion families package.