Green Party co-leader Marama Davidson sang a Māori waiata in Parliament on Tuesday to honour the newborn royal, Prince Louis Charles Arthur.
Prince William Duke of Cambridge and Catherine Duchess of Cambridge welcomed their baby son to the world a week ago.
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Parliament congratulated the couple on their child, who joins his brother Prince George, four, and his two-year-old sister Princess Charlotte in the royal family.
Ms Davidson said she hoped the Duchess of Cambridge found some downtime to "be whatever shape she needs to be in to care for a new baby".
"I wish all children were as celebrated in the House of Parliament in this fantastic way, and every single child was a notice of motion...we can do that in the agenda that we run in this House of Representatives instead," Ms Davidson said.
"I didn't buy a gift, but I wrote a song for my own babies and if the Duke and Duchess would like to learn it and sing it to their baby, they're more than welcome to."
Marama Davidson's waiata:
Ka haere te wā, kua pou te hau
Haere ki te moenga, moe, moe, e
Jiggling your body
Time passes, you've exhausted yourself
Time for bed, sleep, sleep well
New Zealand's official gift to the Royal family was a hand-crafted wool baby blanket featuring a manuka flower and seed pod design, and a selection of New Zealand children's books.