Prime Minister Jacinda Ardern urged New Zealanders to "call out" Covid-19 rule-breakers Monday, as public anger built over a series of infringements that forced the country's largest city back into lockdown.

A frustrated Ardern -- who has won widespread praise for her pandemic response -- said the breaches that led to Auckland being shut down for the second time in a month were intolerable.

She said some people involved in the latest outbreak had ignored clear instructions to remain in isolation and failed to fully disclose their movements to contact tracers.

"Those individuals are facing the judgement of the entire nation, there are consequences, undoubtedly," Ardern told reporters.

New Zealand has recorded only 26 Covid-19 deaths in a population of five million, but Ardern said everyone needed to cooperate in order to keep the virus in check.

"If that means calling a family member or colleague out for not following the rules then we should do that. Do it with kindness, but do it," she said.

The stay-at-home order was imposed in Auckland on Sunday, after it became clear a snap three-day lockdown last month had not halted a cluster of infections in the city of 1.7 million.

Concerns centred on a family where the chain of transmission was unclear, although it has since emerged they had contact with infected members of another family in defiance of isolation orders.

One of those involved visited a doctor, a college and the gym while awaiting the results of a test that eventually showed he had the virus.

Ardern said "we're all paying the price" for their actions.

"Everyone is angry... I totally get that," she said.

"At the same time, how do we make sure people tell us the truth because there is nothing more valuable to us than knowing, in these scenarios, where contact has occurred?"

The Auckland cluster currently comprises 15 cases, 12 of them active, and authorities will be closely monitoring any further infections before making a decision on easing restrictions.

New Zealand's strategy is to eliminate coronavirus by following up every community case with extensive testing and contact tracing, backed where necessary by regional lockdowns.

Authorities have the ability to take enforcement action against rule-breakers, but have yet to issue a single fine for not wearing a mask on a plane or public transport.

Asked if enforcement needed to be more proactive, Ardern said it was an operational matter for the police.

"Politicians aren't the ones that determine enforcement, and that's rightly so," she said.