The latest group 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, 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. Test results should be through within the next few days.
Before people board flights in India they are being checked to see if they are symptomatic.
The journey from India was flown by Air India, with its international crew in managed isolation when they arrived - which is now standard practice, McElnay said. The crew has since left the country.
"I think they were in for two days," McElnay said. "They were transported to managed isolation, [they] stay there and then get back on a plane and returned back to India."
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 23. They were tested because they were a contact of another case and tested positive yesterday.
An infant under the age of 1 is included in today's 12 new cases. The oldest is aged 70+.
Children under the age of 12 months old are not always tested for the virus, and nor do they need to be, McElnay said.
If the parents of the child test positive, it's about how you manage the cases. Whether you add the baby to the total number of cases doesn't change how you manage the cases, she said.
New Zealand has contributed to global initiatives around finding a vaccine. "We're very much part of that global initiative," McElnay said.
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."
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 Organisation.
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," 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.
The Auckland August cluster is not yet considered to be closed.
A "formal and lengthy" process needs to take place before they can confirm the case is closed, McElnay said.
"It's certainly looking very encouraging and hopefully we'll be able to report that it's closed in due course."
The Ministry, along with the All of Government group, are reviewing their plans for any outbreak, resurgence and a range of different scenarios as they move into the summer months.
The process is largely time-focused, with 28 days having had to have passed since the last case tested positive.
"On the basis of what we're seeing at the moment, that would certainly be another 28 days before we could officially close it," McElnay said.
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 they have been.
"This is especially important when on holiday because you may not remember all the locations you've visited," McElnay said.
Good hygiene practices should be maintained, including washing and drying your hands, or using hand sanitiser if you're unable to wash your hands.
There are now 2,287,700 users registered on NZ Covid Tracer app.
The case arrived in the country from France via Singapore on September 25, the Ministry said in a statement.
One person with the virus was in isolation on a general ward at Middlemore Hospital.
Earlier this week, the Ministry said public health services were continuing to contact trace, test, and isolate close contacts of three community cases reported on September 23.
There were a total of 44 close contacts associated with those cases, all of whom are self-isolating. All but one returned negative test results, with one result pending on Tuesday.
The trio is a family group linked to the September 11 chartered flight from Christchurch to Auckland for people leaving a managed isolation facility having completed their 14 day-stay.
Also on the flight was the man who tested positive for Covid-19 at the weekend whose virus is thought to have had a rare three-week incubation period.
Yesterday's new virus case had been transferred to the Auckland quarantine facility. There were 17 people total isolating at the facility from the community, including nine who have tested positive for the virus and their household contacts.
Since August 11, the contact tracing team had identified 4073 close contacts of cases, of which 4073 have been contacted and are self-isolating or have completed self-isolation, the ministry said.
"This number has dropped since yesterday due to records being identified as duplicates in the system.
It comes as the Government has signalled that Bluetooth-enabled tracing tech could be rolled out as soon as November.
The August Auckland Covid-19 outbreak prompted a surge in people using the phone app to scan QR codes for contact tracing, rising from 30,659 to 1.1 million recorded scans within a week.
By the time the city moved out of lockdown, daily numbers had reached 1.7 million - and went on to hit a peak of 2.5 million on September 5.
But since then, numbers have been coming back down, falling to about two million on September 12, 1.5 million on September 20, 1.2 million on Saturday - and just over 975,000 on Monday.
Asked about the trend today, a Ministry of Health spokesperson cited an update to the app, rolled out on September 9, as a "significant factor" in the drop-off.
While the update made the app more user-friendly by removing the requirement to sign in before scanning, it also delayed the reporting of anonymised scan data to the ministry until users logged back into the app.
Dr Andrew Chen, a researcher at University of Auckland-based Koi Tū: The Centre for Informed Futures, believed the key reason was fewer people were bothering to check in.
"While I agree that this technical issue would contribute to the decline in scan counts, I think that the majority of it would be explained by fewer people participating."