New Zealand conceded its ambitious "COVID zero" elimination strategy may no longer be viable on Sunday as an outbreak of the virulent Delta variant spread further.

COVID-19 Response Minister Chris Hipkins reported a further 21 cases in a virus cluster that emerged in Auckland last week, ending a six-month run of no local cases and sparking a national lockdown.

Hipkins said Delta's highly transmissible nature was making this outbreak more difficult to contain than others, raising "big questions" about the elimination strategy.

"The scale of infectiousness and the speed at which the virus has spread is something that, despite all the best preparations in the world, has put our system under strain," he told TVNZ.

New Zealand's widely praised COVID-19 response - which has resulted in just 26 deaths in a population of five million - centres on eliminating the virus from the community.

It has relied on strict border controls backed by hard lockdowns when any cases do slip through, but Hipkins said Delta may force a rethink.

"(Delta's) like nothing we've dealt with before in this pandemic," he said.

"It does change everything, it means that all of our existing preparations begin to look less adequate and raises some pretty big questions about the future of our long-term plans."

Neighbouring Australia has also pursued a "COVID zero" strategy and been similarly frustrated as its Delta cases continue to spike.

The New Zealand outbreak has underlined the country's slow vaccination rollout and prompted accusations the government became lax after its early success dealing with the pandemic.

Only about 20% of the population is fully inoculated, one of the lowest rates in the developed world.

Opposition National Party spokesman Chris Bishop said the outbreak had exposed a lack of urgency in Wellington's vaccine plans.

"The government's complacency and inability to ensure supply and delivery of the vaccine has made us all sitting ducks, completely vulnerable to the Delta variant when it inevitably got into the community," he said.

Another opposition figure, ACT Party leader David Seymour, said Hipkins could not use the Delta variant as an excuse for current failures.

"We've known about Delta since December, what's he been doing in the meantime?" he asked.

Hipkins said elimination remained top priority for the ongoing Delta outbreak, which now totals 72 active cases - 66 of them in Auckland and six in Wellington.

Positive cases have been recorded visited several busy locations, including schools, churches and supermarkets, with health teams checking the status of almost 9,000 close contacts.

The national lockdown is due to expire late Tuesday, although Hipkins indicated Auckland could face further restrictions even if they were lifted elsewhere.

"If I was an Aucklander, I'd certainly be preparing to be at home for a bit longer," he said.

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