"As with our first outbreak, things will get worse before they get better," she said in a televised address.
Ardern was encouraged by the fact that all the cases so far were in a single cluster limited to Auckland.
"You can see the seriousness of the situation," she said.
"While it is serious, it is being dealt with in an urgent but calm and methodical way."
Bloomfield said authorities were urgently exploring all possible routes of transmission.
"We want to find out how large it is as soon as possible, so we've been testing all close contacts, casual contacts, workplace, family-related," he told TVNZ.
"This is what we want to do as quickly as possible to find out how extensive the outbreak is and who the first case might have been."
Freight link 'unlikely'
Auckland's lockdown is scheduled to end late Friday and Bloomfield said any decision on extending it depended on what the investigations uncovered over the next 24 hours.