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There are 71 new Covid-19 cases today in the community, which Director of Public Health Caroline McElnay said was "sobering but not unexpected".
And the number of daily cases is expected to double in the next 14 days.
Deputy Prime Minister Grant Robertson said officials expected case numbers in Auckland would rise, but said "they are rising quickly".
Today's cases are all in Auckland.
Robertson said the reproduction rate (the R value) was somewhere between 1.2 and 1.3 and that meant cases would rise. The R value is the number of people which each case passed the virus to.
Robertson said case numbers would head towards the "triple-digit mark" but believed they could be managed.
He blamed people gathering in other people's homes for the rise in cases and urged everyone to follow alert level 3 rules. He stressed that alert level 3 was suitable for managing the outbreak when asked about the prospect of alert level 4.
"These gatherings inside people's homes are not allowed... my message today is clear. We need people in Auckland to stick to alert level 3 rules."
Robertson said "very few" cases were coming through work sites and the outbreak was affecting people "in all parts of Auckland".
"This is no longer an outbreak about a couple of clusters, and a couple of suburbs," he said.
The country's level of hospitalisations remained relatively low, he said, and ICU capacity "is fine" at the moment, but people need to prepare for that to grow".
"Now is not the time for complacency." He asked Aucklanders to get vaccinated and to not mingle with family and friends, apart from the outdoors.
Robertson said restrictions only worked if everyone followed the rules. "It has never been more important to follow the basic rules".
He hinted that rules could be beefed up if that was required. Prosecutions regarding the "gatherings" were up to police, but they couldn't be everywhere and "that is not the solution to the problem".
"The solution is people obeying the rules."
In Auckland 87% of people had had their first jab - but this number had not increased for several days, he said.
New Zealand had the lowest Covid hospitalisation and death rates in the OECD, Robertson said, but the country needed to stick to tried and true measures to avoid the "carnage" other countries had experienced.
Robertson encouraged all New Zealanders to get vaccinated, and it was particularly important for community leaders to show leadership and get vaccinated. He said the Thames-Coromandel mayor "has views that are not going to help us get vaccinated".
His message for Kiwis waiting for other vaccines was: "Pfizer is a safe vaccine. All around the world millions of people have received it, and it is safe for them. It's the vaccine we are asking New Zealanders to use."
It was still being investigated as to how two Auckland sex workers were able to reach Blenheim and they both have tested negative for Covid-19, he said.
There are no new cases in Waikato today. Yesterday's two cases remain unlinked.
There were 3680 swabs taken in the region yesterday. In Waikato, there was a positive detection in Te Awamutu on Tuesday, and follow-up sample results are still to come through. It's unclear if it's a new case or an old case "shedding the virus".
In Northland, 2145 swabs were taken yesterday and there are no positive cases.
Daily case numbers have being growing in Auckland for the past three days and Covid-19 Response Minister Chris Hipkins acknowledged yesterday that the virus was spreading across the city as an increasing number of locations of interest pop up.
Yesterday there were 53 new cases in Auckland and two in Waikato. On Tuesday, 43 cases were reported in Auckland and three in Waikato and on Monday 35 new cases emerged in Auckland, none in Waikato.
It has been revealed one of two people who tested positive for the virus on Auckland's North Shore is self-isolating in a Kāinga Ora housing complex.
Meanwhile, there are calls for authorities to crack down on rule-breakers as a third Covid positive woman is hiding from police, after fleeing her home in Māngere.
Police said she is known to authorities and The New Zealand Herald understands police have been directed to take her straight to the Jet Park quarantine facility when she is found.
Today the Government outlined plans for hospitals to cope with a surge in cases as the country moves away from an elimination strategy, with worst-case scenarios showing the region including Auckland and Northland could face more than 5000 cases a week in a Covid surge.
Auckland City, North Shore and Middlemore hospitals have already been hit by exposure events.
Two patients and two staff members tested positive after an exposure event at Dialysis Unit adjacent to North Shore Hospital and other staff have been stood down as a precaution. Staff were also stood down at Middlemore Hospital earlier this week after a positive case was detected.
Yesterday there were 32 people with Covid in hospital and six in ICU.