Health Minister David Clark announced the third positive test for COVID-19 had come through late on Wednesday.

The Auckland man, aged in his 40s, has not recently travelled to any coronavirus hotspots but has family members - also New Zealand residents - who have just returned from Iran.

They are now all self-isolating, and the man's partner is also being tested for COVID-19.

Dr Clark said officials had begun tracking the movements of both the infected man and his family members.

A second case was announced on Wednesday morning, a 30-something Auckland woman with a partner who was also displaying symptoms of the virus.

Officials tested their swabs on Thursday and expect results soon.

The family transmission is the first New Zealand case of an infection of someone who has not travelled overseas but Director-General of Health Ashley Bloomfield said it should not spark panic.

"I don't think the genie is out of the bottle ... but there could be transmission happening in the community," he said.

Dr Bloomfield said COVID-19 spread differently to the regular flu, where people could transmit the virus without displaying symptoms.

"It's symptomatic people that transmit that virus (so) if you are unwell with symptoms then stay at home and take precautions," he said.

"I think that's a really key message here."

There have been no confirmed cases of the disease in the Pacific.

Australia and New Zealand are giving support to the United Nations to ready the island nations should the virus land in the developing region.

Foreign Minister Winston Peters has announced a $NZ1 million ($A950,000) contribution to the World Health Organisation's Fiji-based Pacific response plan.

"It is vital that New Zealand is working hard in partnership with our neighbours to ensure the region is safe and as prepared as can be," he said.

New Zealand is also sending teams to the Cook Islands, Tokelau and Niue to provide support.

Australian Associated Press