New Zealand has reported 14 new cases of Covid-19, two days after the country's first four domestic cases in more than three months.

All but one of the new cases were found in Auckland, one day after New Zealand's largest city was placed under a three-day lockdown.

The 13 Auckland cases are all linked to the four family members who were the country's first domestic cases in 102 days, the Ministry of Health said.

The other new case is a woman who arrived to New Zealand from the Philippines on 8 August and has remained in managed isolation since.

Health officials are working to determine how the four family members were infected. Particular attention has been paid to the workplace of one member employed by international cold-storage and transportation firm Americold, which operates two facilities in Auckland where officials suspect the virus may have spread from imported freight.

Ten of the new cases are also linked to Americold. Testing is ongoing among employees of the company's site in Auckland suburb Mount Wellington, where the family member works, and all employees of a facility near Auckland Airport have been tested, the Ministry of Health said.

One of the Auckland cases is a secondary school student. The school has contacted more than 100 students and a handful of staff who are considered close contacts advising them to self-isolate, the Ministry of Health said.

Prime minister Jacinda Ardern noted "the seriousness of the situation we are in" at a press conference on Thursday.

"As we learned from our first experience with Covid: once you identify a cluster, it grows before it slows," Ms Ardern said as she outlined her government's response to the outbreak.

"The whole goal is to get us back to normal as quickly as we can."

New Zealand has gained praise around the world for its swift response to the first wave of the virus, with much of the praise directed at Ms Ardern herself.

Her government has again moved quickly, imposing a strict local lockdown on Auckland alongside nationwide social distancing measures. Ms Ardern is due to confirm whether or not restriction measures will continue and possibly be expanded at 5:30pm on Friday.

Thursday's new batch of cases bring New Zealand's official total up to 1,238 since the beginning of the coronavirus pandemic with 22 deaths.