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Ten of the cases arrived on a flight from India on September 26 on flight AI1354, Director of Public Health Dr Caroline McElnay said.
She said it could be the highest number reported in one day from the same flight and it was possible we could see more cases linked to the flight.
An infant under the age of 1 is included in today's 12 new cases. The oldest is aged 70+.
The group from India tested positive around day three of their time in managed isolation. All have been transferred to the Jet Park Hotel quarantine facility.
The 10 cases were spread out on the plane, sitting between rows 14 and 41, Dr McElnay said.
The theory is that the travellers were infected in India before boarding the flight. Genomic testing was being done and authorities would look to see if anything suggests transmission on the flight.
For the remaining two cases, one arrived on a flight from the United States on September 26, testing positive on day three of their stay.
The 12th case arrived from the Philippines via Taiwan on September 3. They were tested because they were a contact of another case and tested positive yesterday.
Dr McElnay said she appreciated today's number of cases was a lot and it reflected the high levels of Covid-19 that were popping up around the world.
"This also re-emphasises why we have strong border control measures in place."
Asked if she knew how many people had arrived in New Zealand since the latest outbreak from India, Dr McElnay said she didn't have the numbers.
However, the Ministry was looking at pulling together figures to assist with their assessment of high-risk countries.
"We are also looking at pulling the data on recent flights so we can see how that matches up with the level of risk in those countries."
New Zealand now has 53 active cases - 42 have been imported, the remaining were in the community. There are 1492 confirmed cases that have been reported to the World Health Organization.
Fourteen people are isolating in an Auckland quarantine facility from the community, which includes five people who tested positive for the virus.
One person remains in hospital with Covid-19. They are on a general ward in isolation at Middlemore Hospital.
"Since August 11, our contact tracing team has identified 4047 close contacts of cases, of which all have been contacted and are self-isolating, or have completed self-isolation," Dr McElnay said.
The number of cases has dropped from yesterday because some records have been identified as duplicates in the Ministry's system.
Over 5000 tests were completed yesterday, the total number of tests completed nears 1 million.
Dr McElnay reminded school holidaymakers of the importance of remaining vigilant to stop the virus spreading. Anyone who becomes ill on holiday should contact Healthline or their GP.
"If you're told to get a test, do not wait until you get home to get tested."
People should also sign in to places using the Covid Tracer app or by keeping a record of where you have been.
"This is especially important when on holiday because you may not remember all the locations you've visited," Dr McElnay said.
Good hygiene practices should be maintained, including washing and drying hands, or using hand sanitiser.
There are now 2,287,700 users registered on NZ Covid Tracer app.
The app has recorded a total of over 80 million poster scans, and users have created 3,475,327 manual diary entries.