Green Party co-leader Marama Davidson said the Prime Minister having a baby while in office was a "symbolically significant moment" for New Zealand and women in particular.
Mr Peters is now officially acting prime minister and will fulfil that role for the next six weeks while Ms Adern watches from a distance while on maternity leave. The girl arrived at 4:45 p.m. weighing 3.3 kilograms (7.3 pounds).
The pregnancy news late previous year came as a surprise to Ms Ardern, who then had to simultaneously deal with both intense negotiations to form a government and morning sickness. "We're all doing really well thanks to the wonderful team at Auckland City Hospital", the post read.
Benazir Bhutto gave birth while serving as Pakistan's prime minister in 1990, in a totally different political climate, where her opponents used her pregnancy as a reason to demand her dismissal.
Ms Ardern is one of very few elected leaders to have give birth while in office.
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The intervening months have seen a frenzy of excitement from New Zealanders, many of whom took to the web on Thursday to express their happiness. She said she first knew of her pregnancy in the midst of those talks.
She said that after the birth, she hoped to have some quiet time to enjoy as a family.
"Thank you so much for your best wishes and your kindness", she said.
In contrast, Bhutto, fearing she was in danger of being overthrown, travelled incognito to a Karachi hospital, underwent a Caesarean section, then returned to work.
He lodged a privacy breach lawsuit against a government department the day Ms Ardern left Wellington, recently scuttled a major piece of Labour policy and has attacked the leadership of the country's largest company.