A new testing centre has been established in Invercargill, and rest-homes across the country have gone into lockdown.
Yesterday, director-general of health Ashley Bloomfield announced there were four more probable Covid-19 cases - all linked to the community-based cases - as well as one additional case in managed isolation.
Two of the new probable cases were also family of the first case, and two were co-workers of the family, he said. All were showing symptoms.
Health officials were still unsure if the cases of community transmission were linked to staff working at the borders or at managed isolation facilities.
The Government’s response has been praised by University of Otago department of public health Prof Michael Baker, who said it responded "very vigourously, very rapidly".
But the country had to prepare for all possible scenarios, he said.
"Given the timing, incubation period and so on, the virus could have been circulating for a couple of weeks. The extent of that outbreak is the key unknown at the moment," he said.
"We are a mobile population and it’s possible that the virus has been in other parts of New Zealand. Hopefully it’s not, but a regional lockdown only really works when the virus is confined to that population."
At noon yesterday, Auckland moved into Level 3, and the rest of New Zealand went into Level 2.
The restrictions will remain in place until midnight tomorrow.
Prof Baker said there had been some complacency about the virus in New Zealand, but the outbreak in Victoria, Australia, had been sobering.
There was cause for some optimism, as there were "more tools" available to tackle the virus than during the first outbreak earlier in the year.
"We know more about the virus, we’ve got much better testing capability, contact-tracing capability, and the alert level system’s well established, and we’ve got use of face masks.
"They’re all really useful tools that we didn’t have."
A drive-through Covid-19 testing station opened at the WellSouth offices in Invercargill yesterday afternoon to help GPs cope with increased demand.
WellSouth chief executive Andrew Swanson-Dobbs said there had been a significant rise in demand in the South.
"It is exactly what has been requested, but we need to ensure it is people who are symptomatic or who have been close contacts."
At this stage, community-based assessment centres were not being re-established in the district, but they were prepared to do so if required.
Visiting hours for Southern District Health Board hospital remain unchanged in Level 2, but people were asked not to visit patients if they were unwell.
Chief medical officer Nigel Millar said patients presenting at ED and other departments for treatment would notice tighter screening procedures.
Patients who presented with respiratory illness, but were unlikely to have Covid-19, will also be tested as part of ongoing surveillance testing.
Aged-care facilities have gone into lockdown, but palliative care services continued to offer full services.