There are no new cases of Covid-19 in the community and all contacts of the family connected to the latest outbreak have so far returned negative tests.
The Ministry of Health released the information ahead of the Prime Minister and director general of health Ashley Bloomfield speaking at 4pm after the Cabinet meeting.
There are five new cases in managed isolation, the ministry said.
After genomic testing confirmed the family's cases were the UK variant - B1.1.7 - ESR is now scanning the international genome database to see if there is a match.
"This result reinforces the decision to take swift and robust action around the latest cases to detect and stamp out the possibility of any further transmission," the Health Ministry said in a statement.
Yesterday a mother, father and daughter tested positive for the highly infectious UK variant of Covid-19, spurring Auckland into alert level 3 lockdown and the rest of the country into alert level 2 lockdown for 72 hours.
Contact tracing has identified 10 close contacts outside the household. Six of these close contacts have returned a negative test and four results are pending.
Further interviews with the confirmed cases will happen today which could mean the locations of interest could change or be added to.
"The priority is for close contacts and casual plus contacts to be tested so we can understand any risk in the community."
More than 1000 tests from across Auckland were processed yesterday and community testing sites at Health New Lynn, The Whanau Ora Community Clinic in Wiri, Otara Community Testing Centre and Botany Testing Centre are open for more community testing.
For further information on community testing station hours is available on the Auckland Regional Public Health Service website https://www.arphs.health.nz/
A testing site is also available at Papatoetoe High School, the school Case B attended. Please note this testing site is only for students, teachers and their families.
LSG Sky Chefs, where the mother worked, have testing onsite for staff and their families today.
There are also two pop-up testing centres in Waikato - alongside the permanent community testing centre. Those pop-up testing sites can be found at Claudelands Event Centre and Otorohanga Sport Club.
Taranaki Base Hospital, MediCross Urgent Care & GP Clinic, Hâwera Hospital, Waitara Health Centre and Ôpunake Health Centre/Coastal Care are testing centres in Taranaki - where the family visited over Waitangi Weekend.
"It's important the right people can get access to testing — so please don't rush to a centre if you are well, or if you weren't at one of the locations of interest.
"We are anticipating high demand at our Covid-19 testing sites and delays are possible, so our request is to please be patient," the ministry said.
"A reminder that if you were not at a location of interest at the stated times and you have no symptoms you do not need to be tested.
"If you were at the locations of interest at the times stated, you need to get a test, and remain isolated until you receive the result.
"If you have symptoms but have not been to a location of interest stay home and call Healthline for advice.
"As always, if you are unwell with symptoms, take advice about getting tested before you head out – firstly by calling Healthline."
Health officials also reminded Kiwis to use the Covid Tracer app and ensure the Bluetooth function was turned on.
The app now has 2,591,784 registered users and more than 1.1 million people have now enabled Bluetooth.
Of the five cases in managed isolation, one from the United States has been deemed historical.
Three of the confirmed cases returned from India via the United Arab Emirates and Malaysia and the fourth confirmed case is from the United Arab Emirates and flew via Malaysia.
They all arrived on February 13 and tested positive on their day 0 test.
Six previously reported cases have now recovered. The total number of active cases in New Zealand is 47. Our total number of confirmed cases is 1,980.
Officials are hoping to rapidly trace and test people at the woman's workplace - where she handles laundry from international flights - to find the chain of transmission.
They are also ramping up community testing and urging people who were at locations of interest visited by the family to get tested to check for wider community transmission.
Auckland moved to level 3 for at least three days at 11.59 last night, with employees asked to work from home, students urged to stay away from school and police setting up checkpoints at eight locations at the region's border overnight.
Police officers are checking all vehicles arriving and leaving Auckland to ensure there is no non-essential travel. Alert level 2 is less restrictive.
Ardern told Newstalk ZB's Mike Hosking today that the link to the British variant had led officials to think the virus might have come through airport transit or it had stemmed from an international airline crew member.
"We do still have people who transit through New Zealand and fly on to other destinations. They stay airside but of course, it means they are using the things that go through the laundry at this individual's place of work," Ardern told Newstalk ZB.
"The other possibility is that it's international airline crew... they also do the laundry of a couple of international airline crew. And so, that is also one of the possibilities."
It was still possible - but unlikely - the new cases had come from an MIQ case which hadn't been sequenced, said Ardern.