“We are working hard to put together pieces of the puzzle on how this family got infected,” said Director General of Health Ashley Bloomfield.
Investigations were zeroing in on the potential the virus was imported by freight.
Dr Bloomfield said surface testing was underway in an Auckland cool store where a man from the infected family worked.
“We are very confident we didn’t have any community transmission for a very long period,” Dr Bloomfield said during a televised media conference. “We know the virus can survive within refrigerated environments for quite some time.”
China has reported instances of the coronavirus being detected on the packaging of imported frozen seafood.
On Tuesday, the city government of Yantai, a port city in eastern Shandong province, said it had found the virus on the packaging of frozen seafood that had arrived from the port city of Dalian, which recently battled a surge of cases.
Officials said the seafood was from an imported shipment that landed at Dalian, but did not say where it originated.
In New Zealand, Auckland shifted to level 3 restrictions at midday (2400 GMT) on Wednesday, requiring people to stay at home unless for essential trips.
The rest of the country was placed back into slightly looser level 2 restrictions.
The restrictions will initially remain in place until Friday.
“I have huge sympathy ... this is unsettling,” Ms Ardern said. “Stay kind, look after one another.”
Police were setting up roadblocks around the city and supermarkets began rationing the sale of some staple products amid a rush to the shelves. Access to aged care nursing homes was restricted to staff and essential deliveries.
‘The race is on’
The resumption of lockdown measures was reinforced by confirmation on Wednesday that two members of the infected family had visited tourist sites in the town of Rotorua while symptomatic, while a third had gone to work at a finance company in Auckland, also while symptomatic.
Dr Bloomfield said three people at the finance company were showing symptoms of the virus. The business has been closed, with testing underway on other workers.
Health officials were prepared to test tens of thousands of people in the coming days, Dr Bloomfield said.
Panic buying breaks out in Auckland following lockdown announcement
Ms Ardern also delayed a key step toward a 19 September general election, suspending the dissolution of parliament until Monday.
No decision had yet been made on delaying the actual poll, she added, noting there was a window to defer until 21 November.
Siouxsie Wiles, microbiologist and associate professor at the University of Auckland, said lockdown measures were the best option to stamp out the virus.
She warned restrictions would likely be extended if officials could not trace the source within three days.
“The race is on to find the source of the cases and break any chains of transmission,” she said.
People in Australia must stay at least 1.5 metres away from others. Check your state’s restrictions on gathering limits.
If you are experiencing cold or flu symptoms, stay home and arrange a test by calling your doctor or contact the Coronavirus Health Information Hotline on 1800 020 080.
News and information is available in 63 languages at sbs.com.au/coronavirus.