Health authorities are carrying out more than 500 tests for coronavirus each day, in a race to find out if there is now community transmission.
Director-general of health Dr Ashley Bloomfield said the Health Ministry was ramping up testing for Covid-19 to see if it is spreading in the community.
New Zealand now officially has 20 confirmed cases, with a total of eight new cases announced yesterday.
"All those positive tests to date have been people who have returned from overseas," he said.
"We're looking for cases which don't have that overseas link - that would give us an early indication we might have community transmission and then we can go hard."
Bloomfield told Newstalk ZB's Mike Hosking it was still difficult to know if the virus was now being transmitted among communities around the country.
"It's really hard to know. It could be out there.
"One of the reasons that we are testing all those 150 close contacts down in Dunedin to help reassure us and the people of Dunedin that there's not community transmission," he said, referring to the Logan Park High School student who tested positive this week.
Bloomfield acknowledged that New Zealand health authorities had been given a head-start when border restrictions were imposed.
"That's the reason why we've introduced some wider testing, that's the reason the mass gathering restriction has gone in place and I think we'll see other things coming into play as well."
He said that at the moment, those who were only showing Covid-19 symptoms were being tested in order to find those infected.
"We need to test the right people.
"For example, doing 300 tests or so in Auckland means four batches through. The laboratory staff are working through into the night.
"What we want to do is make sure we're testing the right people and finding those positive cases."
SCHOOLS TO REMAIN OPEN - FOR NOW
Meanwhile, Deputy Prime Minister Winston Peters says there is still no need for schools to be closed.
The UK this morning announced that all schools would be shut down and exams postponed.
Peters told Newstalk ZB that New Zealand had not reached that stage yet, however.
The plan was to try to cauterise the issue with the greatest speed. More information was also needed before making a dramatic decision like closing schools, he said.
Prime Minister Jacinda Ardern is expected to make an announcement today banning indoor gatherings of 100 people or more.
Peters said the evidence and information at this time does not suggest that closing the borders is the best idea.
However, he repeated a plea to anyone with family travelling overseas during the Covid-19 pandemic to ensure they did not get stuck overseas.
He said anyone who had family members temporarily overseas should get in touch with them as soon as possible.