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Two of the new cases are in Tokoroa. One new case - of a person who has been hospitalised with the virus - has not yet been linked to the previous cases.
The two Tokoroa are connected to a family member of the South Auckland family which first tested positive this week.
The trip to Tokoroa also included a visit to a Morrinsville rest home - which was reported yesterday. The resident they visited has since tested negative.
"The visit occurred while they were feeling well and before they were aware of any potential exposure or they were infectious."
A bespoke quarantine facility is being set up for the wider whanau of the two Tokoroa cases to help limit the spread.
Bloomfield said the Tokoroa cases were "clearly linked" to the Auckland cluster but he wouldn't pre-empt the advice he would give Cabinet about alert levels.
Thirty-eight people linked to the cluster have already moved into quarantine facilities.
School's shock at virus link
Bloomfield said Mt Albert Grammar, Taeaofou i Puaseisei Preschool, Glamorgan School in Torbay and Auckland's Southern Cross Campus were closed after confirmed cases were linked to them.
Bloomfield also wrongly said that Pakuranga College was closed.
The Ministry of Health apologised for the error this afternoon.
"While there is a casual link, the Ministry is awaiting further test results and at this point no additional public health action is required from the school.
"The Ministry apologises for putting information in the public domain without first notifying the school."
Pakuranga College principal Mike Williams was later told that it does not have a Covid-19 case at the school despite the announcement.
He said the error caused "huge stress in our community" and left him with no confidence in the health system.
"If that's how their system is, it's no wonder we've got Covid," he said.
"It doesn't give you any confidence, does it? Can you have confidence in the Ministry of Health any more? No."
Williams said he did not know whether Bloomfield confused Pakuranga College with another school or not.
"The Ministry of Health system must be really bad, or he can't pronounce Māori words properly, I'm not sure," Williams said.
Williams was in a Zoom meeting when Bloomfield mentioned the college in his 1pm press conference, and his phone and emails "started going off".
"Even my DPs [deputy principals] were asking, 'why didn't you tell us?' I said I would have if I'd known!"
A 'good picture'
Bloomfield said while he was never pleased to see another case, it was good to see they could be traced back to the original family.
"I think we're getting an increasingly good picture ... and the picture we're getting is a very good one."
Bloomfield said the index case - where the infection originally came from - "is still a piece of the puzzle we're looking to fill".
There was some pool sampling happening where there was a low likelihood of a positive result. Tests from Auckland were being prioritised.
Bloomfield said the case in Auckland Hospital was the most recent case so it didn't yet concern him that it was still "under investigation".
Neither Health Minister Chris Hipkins or Bloomfield said they had information about someone being Covid-positive in Wellington, when asked about a Ramen Shop saying they'd had a confirmed case dine there.
Hipkins said they were not going to comment on every speculation on social media.
Hipkins said because officials still didn't know how the original family became infected they were "absolutely scrupulous" with testing at the border, including maritime border.
Hipkins would not answer questions about whether it was unhelpful for the Deputy Prime Minister Winston Peters to broadcast from his Parliamentary office that there'd been a breach at the border.
Peters told Australian media yesterday evening that a border breach was to blame for community transmission.
Bloomfield said it was hard to know whether the church service in Mangere East was a "super-spreader" event because the results hadn't come back yet.
Bloomfield clarified that a "super spreader" was a person who appeared to "shed a lot" of the virus, not a particular event.
Details of today's new cases
Auckland Regional Public Health are tracing close contacts at the three schools which were reported by media this morning - Taeaofou i Puaseisei Preschool, Glamorgan School in Torbay and Auckland's Southern Cross Campus.
All cases connected
All of the cases, so far, are connected, Hipkins said.
"This is good news."
48,000 tests had been processed in the last 48 hours and none show evidence of cases outside of the cluster, said Hipkins.
The lion's share of the testing efforts would continue in Auckland while people in other parts of New Zealand should continue with good hygiene procedures, Hipkins said.
Hipkins said non-symptomatic people or those who aren't in the "high risk" priority group of border workers going to testing stations were slowing down testing.
They should stay at home, he said.
Bloomfield started the briefing with the reminder that: "The problem is the virus, not people. People are the solution."
There was no stigma in having Covid-19.
Bloomfield has also called on people to respect healthcare workers after reports some had been verbally abused and even attacked.
This was "completely unacceptable".
The total number of confirmed cases in New Zealand since the pandemic began is 1251.
When asked why compulsory testing at the border wasn't implemented, Hipkins said it was "a big lever to pull" and they were boring down on high risk people to be tested.
On the Morrinsville rest home, where two people visited before testing positive, the resident and staff members have tested negative. All staff and residents have been tested and the swabs will be processed today or tomorrow.
The chief executive of Pharmac told Bloomfield this morning that some people were stockpiling medicines and he urged people not to do that as it might mean some people could go without.
The primary means of contact tracing is interviewing confirmed cases to re-trace their steps.
Bloomfield to give advice to Cabinet
Bloomfield will later give his advice to Cabinet on whether the alert level restrictions need to change. The current alert level 3 restrictions for Auckland and level 2 for the rest of New Zealand are set to expire at midnight tonight.
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Cabinet is meeting at 3pm, and Prime Minister Jacinda Ardern will announce its decision at 5.30pm today.
On Tuesday, the 102-day streak of no community transmission came to an end after four people in an Auckland family tested positive without any link to overseas travel.
Yesterday, the first results of the mass testing revealed that the cluster had 17 confirmed cases and one probable case, all linked to the family and all in Auckland.
A staffer at cool store facility Americold is among those at the centre of the outbreak.
This afternoon, the Herald revealed there were two new cases of Covid-19 at the coolstore, bringing Americold's total cases to 13 while the Auckland cluster itself grows to 19.
The cluster's travel history includes Rotorua, Taupo and Morrinsville. Mayor of the South Waikato District Jenny Shattock revealed this morning that there was also at least one case of Covid-19 in Tokoroa.
"Unfortunately we have a confirmed case of Covid in Tokoroa and a probable case - plus five others have been tested as some of them are unwell," Shattock told staff.
A preschooler at the Taeaofou i Puaseisei Preschool, opposite the church, has also tested positive. Many of the church's youngest members attend the preschool also.
Also in Māngere East, a 6-year-old pupil at Southern Cross Campus tested positive, as did a student from the Manukau Institute of Technology.
The Covid risk also extended to Auckland's North Shore last night after a student at Glamorgan School in Torbay tested positive, sending the school into lockdown.
Two Noel Leeming stores on the North Shore were also been told someone who tested positive had visited over the weekend.
Cabinet will look at a number factors when it meets at 3pm, including the number of new cases, where they are, whether they can be connected to the existing cluster, and whether the source of infection has been found.
Deputy Prime Minister Winston Peters claimed last night that the source was a breach at a quarantine facility, but Health Minister Chris Hipkins said this morning he was not aware of any evidence of that.
Cabinet will also consider at how compliant Kiwis will be with lockdown rules, and the economic impact of further alert level restrictions.
The Government has been under fire this morning for the lack of testing of the 6000-7000 workers at the border of in managed isolation or quarantine (MIQ) facilities.
Despite weeks of requests, the Ministry of Health has been unable to provide data about the testing of these workers.
Newshub reported last night that, according to its own calculations, about two-thirds of those working at the border in Auckland haven't been tested at all.
MIQ Minister Megan Woods told Newstalk ZB today that those workers had been tested only if they had symptoms. They also had daily health checks.