Just eight Covid-19 tests of people in the community were processed Sunday, prompting the government to look at whether to loosen testing criteria.
Health Minister Chris Hipkins has said he wants an average of 4000 tests a day to make sure the disease has not resurfaced anywhere.
The latest figures from Sunday show there were 681 tests - but 673 of them were of people in isolation hotels, meaning tests from just eight people in the community were processed.
Prime Minister Jacinda Ardern said that was not good enough, even taking the normally slower weekend rates into account.
Yesterday, Cabinet discussed whether the testing criteria needed to change, she said.
"We've set down an expectation with the minister that he will go and work with the Ministry of Health on whatever adjustments are required to see that surveillance testing increase," she said.
A Ministry of Health spokesperson said more people than eight may have actually been swabbed, because tests are not always processed on the same day.
But the spokesperson said says school holidays and lower than normal rates of influenza may have had an impact on testing.
GP clinics and testing centres were swamped last month when cold and flu season hit, with about 10,000 people being tested a day.
Those numbers dropped right back when the ministry changed its testing criteria to say low-risk people with mild symptoms did not automatically need to be tested.
However, Hipkins has said the pendulum has swung too far the other way, with numbers consistently in the 1000s or 2000s.
Guidelines on who to test were changed again last week to encourage more but that has made little difference.
University of Otago professor and epidemiologist Michael Baker said testing in the community was a vital line of defence to detect any failure in border security.
He told Morning Report it was not just about test numbers but about how they were targeted.
"That's covering centres where there are isolation facilities and also testing staff who work there, aircrews and maritime crews."
It was imperative to look and learn from what had gone wrong overseas, to avoid it occurring in New Zealand, he said.
In winter, he said symptoms of Covid overlapped with other seasonal respiratory infections.
"We could be doing 4000 tests a day but it may not be helping much if it is not carefully targeted. Knowing how that testing is distributed is important."