Prime Minister Jacinda Ardern and TV host Clarke Gayford said they would be looking at their baby's future privacy closer to the time of the birth.
On TVNZ1's Breakfast today, host Jack Tame asked if the recent high interest into the birth was a concern.
Mr Gayford said as it gets closer to June they would have more conversations about how it is best to protect the baby, "and to make sure it is shielded from what is to come".
Ms Ardern quipped up saying, "but we can't shield any future baby from this kind of attire", pointing at Mr Gayford's "dad cardy".
When asked about some of the criticism that has arose out of sharing the role of prime minister with being a mother, Ms Ardern said her "job is to prove this hasn't diminished the focus that I have the privileged role of being prime minister".
"People will have a view, and not everyone will be happy, and I totally acknowledge that."