Health officials have contacted 18 passengers seated on a flight near the first person in New Zealand to be diagnosed with coronavirus.

The one person in New Zealand to be diagnosed with coronavirus, who returned on a flight last Wednesday, remains in Auckland City Hospital.

Prime Minister Jacinda Ardern said today that the patient was in a stable condition and improving. The patient's family members were in self-isolation and were showing no signs of infection.

Health officials were still searching for other passengers on the patient's flight and would go doorknocking if required to contact them.

Ardern said the Government was holding off on imposing wider restrictions on travellers arriving in New Zealand as the coronavirus outbreak spreads overseas.

The Government was receiving advice from health officials as to whether there needed to be further border restrictions.

So far, the only restrictions are in place on travellers from China and Iran.

If someone arrived in New Zealand displaying possible coronavirus symptoms, Ardern said they would "of course" be tested.

But she said the Government won't be just testing anyone "just because they have asked".

People would first need to display symptoms of the virus, such as a high temperature.

Ardern repeated her assurance to the public that there was no need to swamp supermarkets, after reports of mass purchases of items including hand sanitisers, water and toilet paper.

"There is no need to stockpile," she told media at Auckland Airport.

Ardern stressed that said New Zealand has an "incredibly robust" pandemic plan.

"We already had a plan in place… to deal with any further outbreak."

Officials have been planning for a pandemic – that plan is "already in place".

Ardern said its response to date has been "textbook".

Meanwhile major supermarkets are working hard to restock sold-out and high-demand items in the way of apparent panic buying after New Zealand's first case of coronavirus was confirmed.

The Ministry of Health confirmed on Friday that a person in their 60s who flew in from Iran on Wednesday is in Auckland City Hospital with coronavirus after being taken there by family.

They are in an isolation ward and public health officials are tracing other people they have been close to, including passengers on the flight.

The patient is said to be "stable and continuing to improve".