Prime Minister Jacinda Ardern provides an update on the new cases in New Zealand – Mark Tantrum/Getty Images

New Zealand officials are scrambling to trace the source of an outbreak of coronavirus, reporting 13 new cases on Thursday.

Long queues of people have formed to escape a renewed lockdown in the country’s biggest city and be tested.

The discovery of four infected family members in Auckland two days ago shocked a country that had not recorded a case of Covid-19 for more than three months, raising some criticism of the government’s handling of the crisis.

New Zealand announced on Thursday that there were 13 new cases in the community, bringing the total number of active cases to 36.

Prime Minister Jacinda Ardern has swiftly reimposed tight movement restrictions in Auckland and social distancing measures across the rest of the country, echoing her early response to the pandemic, which was praised for its apparent effectiveness.

However, doubts over the origin of the latest cases have raised some questions about that strategy.

Officials reported on Thursday that three more people at a refrigerator-storage facility, where one of the family members worked, had tested positive.

Director-General of Health Ashley Bloomfield said health officials were getting “closer every hour” to finding the patient zero of the outbreak.

“We are working flat out to do the contact tracing we need to do and trace back to find out what the source of this infection is,” Mr Bloomfield told Newstalk ZB radio.

Mr Bloomfield raised the possibility on Wednesday that the virus had arrived in New Zealand via freight, given one of the infected family members works in a cool store that takes imported frozen goods from overseas.

On Thursday, he said that was considered “a low possibility”, but did not detail other potential sources.

Some prominent local health experts suggested it was more likely the virus had been quietly spreading in Auckland for weeks, potentially infecting dozens of people.

Ms Ardern said on Thursday that she expected the coronavirus cluster in the country to grow further before slowing down.

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“As we all learnt from our first experience with Covid, once you identify a cluster, it grows before it slows. We should expect that to be the case here,” Ms Ardern said.

Residents of Auckland, home to around 1.7 million people, were given just hours to prepare for the return to level 3 restrictions on Wednesday, requiring people to stay home unless for essential trips.

People in the city reported waiting hours to be tested for the virus, according to local media, and there was a rush to supermarkets to stock up on essentials.

The rest of the country was placed back into slightly looser level 2 restrictions.

The restrictions will initially remain in place until Friday, when Ms Ardern will announce the next steps.

With an election scheduled just weeks away, Ms Ardern was facing criticism from the major opposition party for the decision to resume lockdown measures.

The NZ National Party also wants the September election to be pushed back to November. Ms Ardern has said she will make a decision on the poll before Monday.