New Zealand to raise coronavirus testing levels tenfold after three more positive results

New Zealand will start testing for COVID-19 at rates of 10 times the current regime as it hunts for cases of the virus.

New Zealand Prime Minister Jacinda Ardern has requested Kiwis living in Australia have access to welfare during the pandemic. Source: AP

Prime Minister Jacinda Ardern has defended New Zealand's low rates of testing for coronavirus, saying there is the capacity to lift testing immediately in line with World Health Organization wishes.

Three fresh confirmations on Tuesday means a total of 11 people have tested positive for the virus on Kiwi soil.

That includes an Australian man who was tested in Queensland and flew to Wellington before discovering his positive result, much to the chagrin of locals.

Tuesday's new cases include two men from a Wellington family and a Dunedin man - the first confirmed spread to South Island.

The Dunedin man has family members with COVID-19 symptoms, who are all self-isolating.

All Kiwi cases have been linked to overseas travel, and none currently require hospitalisation.

However, there are fears that New Zealand's low testing rate could be masking a bigger number of cases - and possible community transmission of the disease.

Health officials have tested just 584 individuals as of Tuesday, with just 60 in the previous 24 hours.

In contrast, Australia's New South Wales - which has recorded 171 positive results as of Monday - has conducted around 25,000 tests.

Ms Ardern denied New Zealand's regime was too limited, saying around 500 tests were currently being processed.

"Our testing has been significant," she said.

"We're ramping up to have the ability to have up to 1,500 tests per day.

"We have the capacity and we are continuing to build capacity."

The Ministry of Health says it currently can conduct 770 daily tests, and Ms Ardern urged doctors to use them.

"If you believe you need to test, test," she said.

We have the ability to test far more than we are now ... we have built the space for those doctors and clinicians to test and they should."

Ms Ardern has come under sustained pressure from the opposition National Party, which believes the government has been too slow to ramp up testing.

World Health Organization Director-General Tedros Adhanom has called on countries to test as widely as possible for the virus.

"You can't fight a virus if you don't know where it is. Find, isolate, test and treat every case, to break the chains of transmission," Dr Adhanom said.

"Every case we find and treat limits the expansion of the disease."