New Zealand's Prime Minister Jacinda Ardern has ordered the country's biggest city Auckland to go into lockdown after the discovery of three new local cases of Covid-19.

The measures will last three days and require residents to stay at home.

Ms Ardern said the country was going "hard and early" after the cases were identified.

New Zealand has won widespread praise for its handling of the pandemic, going months without community transmission.

The country closed its borders entirely to almost all non-citizens or residents early on in the pandemic, aiming to eliminate the virus.

New Zealand, with a population of five million, has recorded just over 2,300 cases of Covid and 25 deaths.

The measures in Auckland require its 1.7 million residents to stay at home except for essential shopping and work. Schools and non-essential shops will close, and entry in and out of the city restricted.

Ms Ardern said three days should allow the government to get more information and get more testing done, and would also help determine if there was any community transmission.

"New cases of Covid-19 in the community was something none of us wanted to happen," Auckland Mayor Phil Goff said, adding the restrictions were the "best way to stamp out the virus".

The rest of the country moves to a higher level of alert, with schools and businesses remaining open but people encouraged to find alternative ways of working if possible.

The lockdown forced the postponement of two races in sailing's America's Cup, one of the few major sporting events with no restrictions on spectators.

The three community cases were announced earlier on Sunday - a mother, father and daughter from South Auckland.

It is unclear how the three contracted Covid. The mother works in the laundry department for an airline catering facility, while New Zealand media said the father was a self-employed tradesman.

New Zealand's Director-General of Health Dr Ashley Bloomfield said his team was "working under the assumption that it is one of the new variants".

He added that the initial focus on investigations was the mother's workplace "because of its obvious connections to the border".

Opposition leader Judith Collins urged New Zealanders to follow the advice of health officials.

But she called for border workers to be vaccinated, saying: "If this proves to be another border failure that is unacceptable. Our border should be rock-solid by now."