Testing for Covid-19 has not been wide enough, and the infection rate is probably much higher than official figures, the opposition party says.
Prime Minister Jacinda Ardern is reassuring New Zealanders there are plenty of tests available for whoever needs it, but National says the criteria are still too strict.
The World Health Organisation has criticised countries for not being aggressive enough with testing regimes.
About 530 tests have been done in New Zealand so far. Eight people have been found to have the virus, and two people remain probable cases.
But National Party leader Simon Bridges says the number tested should be much higher.
"We should be in the thousands, and I think that's why, frankly, we only have eight cases, when I think everything we are seeing around the world is telling us it would be more than that realistically.
Bridges said he believed the process for being tested was too difficult.
"It's a situation where you have to go on a help line for hours, you're then told to contact a doctor, and you have to have symptoms or close contact [with someone] - I say it should be either of those.
"It's not right that people with all the symptoms aren't being tested, when we want thousands to be tested so we have the best information and we can make the best decisions," he said.
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Bridges noted the situation of Cabinet minister and New Zealand First MP Tracey Martin, in isolation after sitting next to Australian politician Peter Dutton for an hour, who tested positive.
But Ardern said anyone who needed to be tested, can be.
"Our capacity is significant. We're ramping up to have the ability to have up to 1500 tests per day.
"And that test number that you've been seeing per day happening in the community is growing day on day."
Health Minister David Clark said hospitals were well prepared for an increase in cases.
"Certainly we are doing preparations for a lot of different scenarios.
"We've seen overseas systems put under pressure primarily because they haven't done the stuff the WHO again emphasised as important today," he said.
Bridges also questioned whether the police had enough legal authority to detain people not sticking to self-isolation rules.
He said National would work with the government to pass legislation to make that authority clear.
Police Minister Stuart Nash said it was something that was still being worked through.
"But the Prime Minister has made it very clear, obviously, if tourists to this country don't self-isolate then she will absolutely consider deporting them," he said.
- If you have symptoms of the coronavirus, call the NZ Covid-19 Healthline on 0800 358 5453 (+64 9 358 5453 for international SIMs)