Ardern, who turned 38 last week, became New Zealand's youngest prime minister and its third female leader when she was elected last October.
"I absolutely accept this layer of interest because it's not our normal yet".
Ardern also plans to bring her baby to parliamentary debates and to the United Nations.
A spokesperson from the centre says, "Our prime minister is already an expert at multi-tasking as she rocks her baby and runs a country!"
"So it's our job to make sure that we are serving the needs of people, regardless of whether they have time to engage with what we're doing or not", she said.
"All of the things that people said that I would experience: that idea that you suddenly have this new person in your life that you could love so much and that time will go incredibly quickly, but that the nights will seem incredibly long, all of that has been true", she told Radio NZ. "It's really an individual choice for each parent, I think".
Ardern told stuff.co.nz they would travel as a family to the United Nations in NY, where she is due to speak.
Ardern started working from her Auckland home on Thursday.
Her return to leadership has spawned countless interviews with the New Zealand press.
Ardern fell pregnant with her first child just three months after taking office.
Her first week back will be focused on "furthering our work in the mental health space", environmental issues and trade-related matters, she said.
US President Donald Trump has signed legislation that will make it easier for New Zealanders to trade or invest in the world's biggest economy.
"I'm getting sleep mostly because I'm sharing the load with others, and I'm very grateful for that", she said.
She officially took back the reins from her deputy Winston Peters at midnight.
Ardern said the U.S. is critically important to New Zealand's interests and the act will help develop closer economic ties. She said the country may need to finish working through its process of addressing historic injustices committed against indigenous Maori before it could sever its constitutional ties with Britain, whose Queen Elizabeth II remains New Zealand's head of state.
"A quick hello as we get ready to come back", the new mum says in the video, which has been viewed nearly 200,000 times.
"I'm privileged, I'm very, very lucky".