Prime Minister Jacinda Ardern has condemned the attack, which left three people in a critical condition, as "despicable" and "senseless".

The shock incident took place on Friday afternoon at a Countdown supermarket at New Lynn, a southwest suburb of Auckland.

Police Commissioner Andy Coster said the man, who was under constant surveillance because of his radical ideology, carried out the attack around 2.40pm.

Mr Coster said trailing agents did not suspect he would act, believing it was "a normal shopping expedition".

Police believe the man grabbed a knife within the store before stabbing nearby men and women.

Mr Coster said police acted "with great courage", shooting and killing him around 60 seconds after the attack to "prevent further injury in what was a terrifying situation".

Police said the man was a "lone actor", and there was no ongoing threat to the public.

St John said three patients were in a critical condition at Auckland City Hospital.

A further three patients - one in a serious condition and two in moderate conditions - were also taken to hospitals across Auckland.

Few details about the attacker have been released due to court suppression orders.

However, Ms Ardern said the "violent extremist" was a Sri Lankan national who arrived in 2011 and was on a terror watchlist from 2016.

"Agencies were using every single possible means available to them to protect the New Zealand public from this individual. Every single possible means," she insisted.

"It was senseless and I'm so sorry that happened."

Newshub reports the man yelled "Allahu Akbar" as he attacked.

Ms Ardern said she did not want to see a backlash against any community from the incident.

"What happened today was despicable. It was hateful. It was wrong," she said,

"It was carried out by an individual, not a faith, not a culture, not an ethnicity,, but by an individual person who was gripped by ideology that is not supported here.

"He alone carries the responsibility for these acts."

Australian Prime Minister Scott Morrison is among those to offer his support to New Zealanders in the wake of the terror attack.

"Australia condemns the horrific terrorist attack in Auckland. Our thoughts are with all those affected," he said.

"We stand with our Kiwi family in deploring all such violent acts designed to create fear and divide us. Kia kaha New Zealand."

The attack is New Zealand's most violent terrorist act since the Christchurch mosque shootings in 2019, when 51 worshippers were killed in a premediated attack carried out by an Australian white nationalist.

The imam for one of two mosques targetted on that day, Gamal Fouda, said Friday was New Zealand's "darkest day" since then.

"It's a horrible thing ... not just for the Muslim community but for all New Zealanders," he told Stuff.

"This person is not understanding of what our religion is about."

Frightening first-hand reports have emerged in the hours since the attack.

Michelle Miller, a resident of nearby Avondale, told Radio NZ she saw a man "running around with a knife, then he just lost the plot".

"It's horrific. I feel sorry for the Countdown staff, I feel sorry for the people who were actually hurt here today," she said.

Countdown spokeswoman Kiri Hannifin said staff were "devastated" by the attack.

"Our hearts are heavy knowing what our team and customers have witnessed and been through," she said in a statement.

New Zealand is currently in a national lockdown to fight a COVID-19 outbreak, with Auckland at strict level four settings.

Australian Associated Press