"Plainly everyone is paying the price," Ardern said about the people's breaches.
The contact happened on the morning after the family was told to isolate, Ardern said.
"No one in Cabinet ... thinks that this is tolerable. What has happened here is a clear breach and everyone is frustrated by it," said Ardern.
But it wasn't for politicians to make decisions about prosecutions.
Director general of health Dr Ashley Bloomfield said at the conference he wasn't aware if the first family has said why they didn't disclose the contact with the most recent cases - but often people could forget or were fearful.
At the same time, she also reminded workers and employers about the Leave Support Scheme and said no one should feel like they have to go to work if they need to self-isolate.
The isolation check-ups also include welfare checks if people need more.
Ardern said "zero complacency, kindness and teamwork" would ensure the virus was "squashed" again.
Asked about the more than 150 contacts of one of the latest cases, Ardern said they'd "always anticipated" there to be large numbers of people involved in the outbreak with someone who'd been moving around for a week and with the places they'd been visiting.
On Sunday morning, Auckland was put back into level 3 lockdown and the rest of New Zealand is at level 2.
Meanwhile, there were no new community cases of Covid-19 reported today and one case in managed isolation.
The last community case reported is Case O which is a household contact of Cases I, J, K and L who all are in the Auckland quarantine facility. Case O was reported last night.
They were moved to the Jet Park Hotel as a precaution on February 23 so were in quarantine during their infectious period which means there is no risk of spread in the community.
Case M and N have also been moved to the Jet Park along with their other household family members.
