A Deash-inspired terrorist stabbed six people at an Auckland supermarket  before police who had him under surveillance shot him dead, New Zealand Prime Minister Jacinda Ardern has said.

"What happened today was despicable, it was hateful, it was wrong," she said, describing the attacker on Friday as a Sri Lankan national who arrived in New Zealand in 2011.

"A violent extremist undertook a terrorist attack on innocent New Zealanders," Ardern told a briefing.

The attacker had been a "person of interest" for about five years, she said.

The man was killed within 60 seconds of beginning the attack, she said, adding that he had been inspired by the Islamic State militant group.

"It was hateful, it was wrong. It was carried out by an individual, not a faith," Ardern said. "He alone carries the responsibility for these acts."

'He's got a knife'

A video posted on social media showed shoppers in the New Lynn supermarket shortly after the attacker struck.

"There's someone here with a knife ... he's got a knife," a woman can heard saying. "Somebody got stabbed."

A guard asked people to leave the shopping mall shortly before about six shots rang out.

Of the six wounded people, three were in critical condition, one in serious condition and another in moderate condition, the St John ambulance service said in a statement to Reuters news agency.

New Zealand on alert for attacks

Witnesses told reporters outside the mall they had seen several people lying on the floor with stab wounds. 

Other said they heard gunshots as they ran out of the supermarket.

Videos posted online earlier showed panicked shoppers running out of the mall and looking for cover.

New Zealand has been on alert for attacks since an Australian terrorist killed 51 Muslims at two mosques in the city of Christchurch on March 15, 2019.

In May, four people were stabbed in a supermarket in Dunedin on New Zealand's South Island.