Asked if Peters would be a good Governor General, Ardern said no former politician should have the job.
"I take a view that the Governor General position, as important as it is, is not rightly held by past central government politicians. It has only happened once in our history, and at that time that was quite controversial. I'd rather remove that controversy.
"There is any number of fabulous candidates. It's a no to any past central government politician, and that's a position I've held for some time."
The Governor General is the Queen's representative in New Zealand, and the country's head of state.
It is traditionally somebody apolitical.
The only politician to also become Governor General was former Prime Minister Sir Keith Holyoake. Holyoake was appointed Governor General by Sir Robert Muldoon from 1977 to 1980, after being Prime Minister from 1960 to 1972.
It caused controversy because the Governor General was traditionally an apolitical role – as a result Holyoake's term was for a shorter three-year period rather than the usual five.
Asked it was time for New Zealand to have its first Māori Prime Minister, Ardern said she believed it was "only a matter of time" before that happened.
She would not pick which of Labour's 15 Māori MPs she thought would do a good job of it.
Ardern spoke after the Dawn Service and her now traditional Waitangi barbecue breakfast: a tradition that has grown for a two barbecue affair to about 20 – and now caters for 2500 people.
Ardern said the idea was borne from her own fondness for a bacon butty, although the demand was now so high that she often missed out herself. "We've always struggled to anticipate the actual numbers we'll have."
She said she was heartened to see the enthusiasm of the hundreds who went to the Dawn Service. She said she had expected to see lower numbers, because of the concern about Covid-19.
That had seen the Waitangi National Trust opt to hold the Dawn Service completely outdoors this year, rather than the dignitaries going into the whare on the Treaty grounds. Ardern said she had welcomed that, as it had given a greater sense of the crowd and atmosphere.
"It was fantastic environment."
"Every Waitangi Day is a chance to reflect on the last year, how we are progressing, our partnership and relationship – but also constantly looking forward with hope."
Ardern has never been to Te Tii Marae, but said she was open to it if that was decided a Prime Minister should return.
