Prime Minister Jacinda Ardern told RNZ's Morning Report one of the new cases is a nurse at Auckland Hospital.
"The health workforce are very well versed and mapping these issues and have done in the past.
We have had COVID-positive cases in our health workforce before. What's different on this occasion is that we have this individual who is fully vaccinated."
Ardern said the four new cases were the workmate of the 58-year-old Devonport man and the workmate's close or household contacts.
She said Auckland Hospital was taking all the precautions they normally would.
"They are stopping movement between wards, testing all staff and patients on wards where that individual worked."
"It confirms level 4 is the right decision," Ardern said.
"These measures have worked before and they will work again."
Testing may give more information about a potential source or connection to the border, Ardern said.
"Once we get genome information that then starts to help helping us to narrow down potential sources, but it's not something I can provide further information on now, we will be looking to give an update at 1pm, if we can."
Any decision on longer lockdowns would be affected by how widespread the infections are, she said.
"If we identify the source was potentially a case from some distance from where we've identified this community case, that then gives you a bit of an idea of how many others may be affected.
"Whether or not we've got potentially unknown cases that are further away from the eventual index when we find it - that will be the kind of information we're looking for to make those decisions."
The new cases were not necessarily surprising, she said, with previous variants not everyone a case was in contact with would become infected nor even all their household members but the likelihood of transmission of the Delta variant is much increased.