New Zealand has extended a lockdown of its largest city Auckland by at least 12 days, Prime Minister Jacinda Ardern announced, as authorities struggled with a growing new coronavirus outbreak.

"Cabinet has agreed to maintain our current settings for an additional 12 days, bringing us to a full two weeks in total," Ms Ardern said.

It comes as health officials say the country's resurgent coronavirus outbreak has spread beyond Auckland, in a significant setback to efforts to contain the infection.

Health Minister Chris Hipkins said there were 12 more cases of community transmission, and one probable, following the surprise re-emergence of the virus in Auckland this week.

He said two of the infections were found in the North Island town of Tokoroa, around 210km south of Auckland.

The infections outside Auckland come despite a strict lockdown in the city, including masked police blocking roads to seal its borders.

Mr Hipkins played down fears the failure to ringfence infections to Auckland meant the virus could now be rampant elsewhere.

He said: "All of the cases so far are connected, they are all part of one Auckland-based cluster, that's good news," adding that the Tokoroa cases were identified quickly.

"We've seen no evidence of a Covid-19 case outside of Auckland that is unrelated to the cluster we are dealing with."

The crisis erupted when four family members in Auckland returned positive tests on Tuesday, ending New Zealand's run of 102 days with no reported community transmission.

Ms Ardern said that genetic testing had shown no link between this outbreak and cases in quarantined arrivals from overseas, or from the first wave of cases.

But she voiced optimism that the latest outbreak had been quickly detected and could be brought to heel.

"There are signs we have found this outbreak relatively early in its life," she said.

"Extensive testing and contact tracing" had determined the earliest case becoming sick around 31 July.

In just four days, New Zealand has gone from a transmission-free haven to contemplating national lockdown.

National health director-general, Ashley Bloomfield, acknowledged feelings were running high but urged the public not to take out their frustrations on frontline health workers.

He said: "We've had reports of healthcare workers, who are doing their best to provide testing for people, being verbally abused and even attacked.

"This is completely unacceptable."