With Prime Minister Jacinda Ardern due back at Parliament soon, Speaker Trevor Mallard has laid down some strict rules to media on taking photographs or filming her daughter Neve.

Ardern's family, including partner Clarke Gayford and baby Neve, will be moving into Wellington's prime ministerial residence Premier House near the Beehive next week.

After speaking to Ardern, Mallard has issued a warning to political media that any filming or taking photos of Neve, even if inadvertent, could result in being stripped of their right to be at Parliament.

Mallard is keen to make Parliament more family-friendly and has been snapped with the children of other MPs in posed photos.

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There are seven MPs with babies: Labour's Ardern, Kiri Allen, Willow-Jean Prime and Kris Faafoi and National leader Simon Bridges and MPs Tim van der Molen and Chris Penk. Two more are expecting new babies soon – Labour's Chris Hipkins and Green MP Julie-Anne Genter.

Prime, whose daughter Heeni has been a familiar sight around Parliament, said she had never objected to her baby being filmed or photographed on the precinct.

"The general approach is that they've usually come to me to ask me if that's appropriate and if that's okay. It's really an individual choice for each parent I think. Some choose to share their children and their family with the public and others keep it private and that's absolutely a personal choice."

Green Party co-leader Marama Davidson, who has six children, said she wouldn't bring them to Parliament if she didn't want them in the public eye, knowing that media were around.

"If I did have an objection I would go back and ask, I would prefer for my child not to be featured."