It is further positive news as the country awaits today the majority of test results from Papatoetoe High School - and with it, future of Auckland's snap level-3 lockdown and the rest of New Zealand's level-2 restrictions.
The Auckland family - a mother, father and daughter who have tested positive - have what are considered 42 close contacts. Thirty-three of them are students and teachers from the high school and nine are non-high school close contacts.
Eleven of these 42 people returned negative tests yesterday, and a 12th - another school test - came back negative last night.
Bloomfield told Newstalk ZB's Mike Hosking that if all of the close contacts came back negative "that would reduce the likelihood" Covid-19 was widespread in the community.
But he wouldn't go so far as to say New Zealand would be in the clear. "We're not done, what we are is reassured that there hasn't been any onward transmission from our current cases. The other thing we're really looking for - because we're not sure exactly where this infection has come from - is are there any parallel sort of chains of infection or chains of transmission out there in the community.
"So the wider testing in the school, and in the workplace and the community, and in particular those places of interest is what we're really looking at as well."
Separately, seven of nine close colleagues of the mother - who works at airline food and laundry provider LSG Sky Chefs - have returned negative tests so far.
The mother is considered the most likely of the three family members to have contracted the virus first although that has yet to be confirmed.
Bloomfield said officials were keeping an open mind to the source of the infection because the daughter developed symptoms before the mother.
"The important thing about a source is keeping an open mind and not to jump to conclusions, just because the mother works around the airport precinct is not to say 'oh that's where it's come from'. One of the interesting things here is that the daughter reported onset of symptoms before the mother. So we have to be open-minded that she could be the first case, and could have got it somewhere else. And that's what we're trying to track down."
Onward spread and whether the source of the infection has been found - or narrowed - would be the key things Bloomfield will be looking at when he writes his advice for Cabinet tomorrow on alert levels. "By the end of the day we'll certainly have a lot more information."
More than 3000 people were tested yesterday and the bulk of those results would come back today.
Those results will help determine if Auckland's lockdown is a short, sharp affair - perhaps over as early as tomorrow night - or whether the country is dealing with a bigger community outbreak of Covid-19.
Health experts are still striving to pinpoint the source of the UK variant which has infected the Auckland family.
Hundreds of people were tested at a pop-up testing station at the school yesterday. The school's principal, Vaughan Couillault, expects 3000 tests to be administered over Monday and today, and urged patience for those waiting up to two hours in line.
News yesterday of no new active Covid-19 cases connected to the family came as "heartening" news to Prime Minister Jacinda Ardern but she is waiting until today's mass-testing results before she gets too comfortable.
"We do want to give it that bit more time before we get too far ahead of ourselves," she said last night.
Bloomfield was also pleased, saying yesterday's reported Covid numbers were an "encouraging sign".
But, like Ardern, he will be keeping a close eye on today's test results – particularly those from the school – before he gets too excited. "It is the days ahead that will be crucial."
For the most part, Ardern said Auckland's first day back at alert level 3 had gone "smoothly".
This is despite some reports of long lines of cars with people waiting to be tested – some as long as two hours.
On Sunday, Ardern announced Auckland would go back into alert level 3 until at least Wednesday at 11.59pm. The rest of the country would be at level 2 over the same period.
Ardern confirmed yesterday there had been no changes to the alert level settings but did reveal the new community cases were the more infectious UK strain.
Bloomfield said this was a "tumultuous period" for New Zealand and that "Covid-19 can feel like being on a roller coaster that you haven't actually bought a ticket for".
But both he and Ardern were upbeat about the latest vaccine developments.
The first batch of roughly 60,000 Pfizer Covid-19 vaccines arrived on New Zealand shores yesterday morning.
Ardern said this would be "more than enough" doses to vaccinate New Zealand's frontline workforce over the coming weeks.
From here, smaller batches will continue to arrive while the newly arrived vaccines are tested for "quality assurance".
Ardern, however, remains confident the first jabs will be administered this Saturday. By then, the plan is for Auckland to be out of level 3.
But there are still a number of hurdles to overcome.
"What we really want is the results of this testing at the school, at the workplace and in the wider South Auckland community to really rule out that there isn't undetected trains of transmission," Bloomfield said.
