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".
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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".
However, in the way of the announcement that the potentially deadly virus was present in New Zealand, Auckland supermarkets were hammered by customers stocking up on essentials like toilet paper and water.
At some stores, queues were out the door and people even lined up before opening.
Hand sanitiser has been unavailable at supermarkets for days due to the coronavirus scare.
A shopper at one Pak'nSave supermarket on Friday night said it was as if people were "stocking up for the apocalypse".
This morning a Foodstuffs spokesperson assured customers that the company was working hard to make sure essential items were available.
Foodstuffs own major supermarkets Pak'nSave, New World and Four Square.
"We have been prioritising deliveries over the weekend to stores which have seen increased customer demand," the spokesperson told the Herald.
"Since the coronavirus has emerged globally, demand for products including hand sanitiser has significantly increased.
"We're working with suppliers to secure more stock as soon as possible, but volumes are limited due to international demand.
"Customers can expect stores to be out of stock completely or to have quantity limitations in place."
The spokesperson said if customers continued to shop "normally", stores would have no issues providing "the usual range of products".
"We would ask customers to resist the urge to stock up as this simply puts unnecessary pressure on stores," they said.
There had also been an increase in online shopping at Foodstuffs supermarket chains.
Countdown general manager of corporate affairs, quality, safety and sustainability Kiri Hannifin was reluctant to comment but gave a short statement.
"We would urge customers not to stockpile," she said.
"There's no need to panic and we have systems in place and are working with our suppliers to manage demand so that we can provide the essentials that Kiwis want.
"We're also monitoring products, our stores and online shopping throughout the day and getting stock into stores as best we can.
"We'd reiterate that stockpiling isn't necessary and we'd encourage customers to simply shop as they normally would."
Prime Minister Jacinda Ardern also weighed in, telling the public to continue with everyday life.
"If you need a bottle of milk, go and get it. If you don't, do not react in any other way than you would any other day," she said.
"The public should be going about their daily lives."