Jacinda Ardern cuddles one-week-old baby Neve

New Zealand Prime Minister Jacinda Ardern looked every bit the doting mother as she cuddled her one-week-old baby Neve in a live Facebook video on Sunday.

Despite being on six weeks maternity leave, the 37-year-old couldn't help but excitedly talk up her government's new $5 billion welfare package for families.

'This is the thing I am most proud of,' Ms Ardern said as she discussed the 'significant' welfare changes while holding her 'human hot water bottle'.  

Ms Ardern, 37, and partner Clarke Gayford welcomed baby Neve Te Aroha Ardern-Gayford to the world on June 21. 

'Welcome to our village wee one,' the New Zealand prime minister posted on Instagram

'Welcome to our village wee one,' the New Zealand prime minister posted on Instagram

Ardern explained that some elements of the package were first designed on the floor of a friend's home.

She then went on to say that families with newborn babies would be granted $60 a week thanks to the implementation of the package.

After expressing her enthusiasm for the new package, she took a moment to let her followers know how she was finding being a new mother. 

'I promise, I'm not too bad, I

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