The failure to identify any new cases has also grown hopes that Auckland's three-day lockdown will end on Wednesday night, without the need for further restrictions.

More than 15,000 tests were taken on Monday after three family members tested positive to the virus on the weekend.

Of the 5818 to have been processed, none have come back as positive, prompting COVID-19 Minister Chris Hipkins to declare himself "very pleased".

"A day when we get zero positive test results is always a good day," he said.

New Zealand's cabinet will meet on Wednesday afternoon, armed with the latest case data, to decide on the future of Auckland's lockdown.

"We're going to be looking at testing numbers, we're going to be looking at what that's telling us ... and whether there's more information about our source investigation," Mr Hipkins said.

Jacinda Ardern's government placed greater Auckland at alert level three after the discovery of the recent cases, with the rest of the country raised to alert level two.

The latest community cases have brought to light deficiencies in New Zealand's testing regime.

Director General of Health Ashley Bloomfield reported that of 109 close contacts identified of the recent cases, just 33 had been processed as negative by noon on Tuesday.

There are also concerns testing at managed isolation and quarantine (MIQ) is not up to scratch.

MIQ workers are tested at different rates according to their risk levels, with prominent scientists and the opposition calling on tests - where possible - to occur daily.

Mr Hipkins said there were logistical challenges to doing that, but the government was looking at incorporating less invasive saliva testing as used in Australia.

"It's not just about the lab's capacity to process it, it's about the nursing workforce to be able to take the tests," Mr Hipkins said.

"In our MIQ facilities there's a limited number of people willing to do that work."

Australian Associated Press