A man who tested positive days after leaving managed isolation with two negative results has now passed it on to two people in his household.
One of the people he infected is a child at a primary school in Auckland's Mt Roskill, which says it remains safe for children to attend.
However, the school was undergoing a "deep clean" on Sunday as a precaution to reassure parents.
The latest community cases raise questions about whether the two-week isolation period is long enough to remove the risk of returnees spreading Covid-19 into the community.
The Ministry of Health is now investigating whether the man was infected during his flight from India and the virus had an extremely long incubation period, or whether he caught it during his flight from Christchurch to Auckland after leaving managed isolation nine days ago.
There were four new cases of Covid-19 on Sunday - including two not linked to the Auckland cluster but to the returnee from India.
The man arrived in New Zealand from India on August 27 and completed managed isolation, returning two negative tests at the facility in Christchurch before returning home to Auckland on September 11.
He was then tested after developing symptoms on September 16 and returned a positive result.
He and those in his household self-isolated as soon as he developed symptoms and when he returned a positive test they were all moved into the Auckland quarantine facility on September 18.
All identified close contacts have also been isolated and tested, a statement from the Ministry of Health said.
The ministry said the source of the case's infection was still under investigation, but genome sequencing is consistent with two confirmed cases from the same flight from India to New Zealand that landed on August 27.
"It is possible that this case was infected during that flight and has had an extremely long incubation period – there is evidence that in rare instances the incubation period can be up to 24 days," the statement said.
"This person developed symptoms 21 days after he arrived in New Zealand. If this is the case, it sits well outside the standard incubation period of the virus.
"Another possible scenario is that the case may have been infected during the flight from Christchurch to Auckland – other passengers from that flight are currently being contacted and assessed as a precautionary measure in order to exclude them as the source of infection."
The flight was a Government chartered flight and the other passengers were also returnees from Christchurch managed isolation facilities.
Meanwhile, it has emerged that one of the man's close contacts who became infected is a child from Three Kings School in Mt Roskill.
Parents at the school received an email from Auckland Regional Public Health on Sunday telling them a child had tested positive, but was not at school while infectious.
"The school remains open and safe to attend," the letter from Auckland Regional Public Health Service (ARPHS) said.
It was very unlikely there was any exposure to the virus at the school and students and staff do not need to stay at home or get tested unless they have any symptoms, a spokesperson said.
"There is only one close contact in the school community, someone who was not exposed at school. They are currently in self-isolation."
Public Health is monitoring the student's health and will provide clearance when the student can return to school.
Three Kings School principal Moira Blair said they were taking ARPHS' advice that the school could remain open.
"To help reassure our school community, we are having the school deep cleaned today and will be open tomorrow.
"We do want to thank our school community who have been excellent in adapting to the extra measures we have had in place during the pandemic, and continue to do their part."
Sunday's Ministry of Health update was delayed until about 2pm.
The ministry said most people who are infected with Covid-19 will become unwell within 14 days.
"Having returnees stay in managed isolation for 14 days remains the gold standard, and this is also the approach adopted by other countries. Our own modelling confirms that 14 days spent in managed isolation with two tests leaves a very low risk that someone will leave managed isolation with Covid-19.
"Another possible scenario is that the case may have been infected during the flight from Christchurch to Auckland – other passengers from that flight are currently being contacted and assessed as a precautionary measure in order to exclude them as the source of infection.
"This case is another example of the tricky nature of the virus, and a reminder that anyone who has been through a managed isolation facility should remain very aware of their health. Anyone who develops symptoms of Covid-19 should get tested and self-isolate while awaiting results as these people did.
"The first imported case reported today is a man in his 30s who arrived from London via Dubai on September 16.
"He tested positive at routine testing around day 3 of his stay in managed isolation at the Novotel Ellerslie, and is being transferred to the Auckland quarantine facility today.
"The second imported case reported today is a man in his 20s who arrived from India via Singapore on September 12. He returned a negative test for Covid-19 around day 3 of his stay in managed isolation at the Grand Millennium.
"The man was moved to the Auckland quarantine facility as a close contact of a confirmed case, retested, and has returned a positive result."
There are 47 people isolating in the Auckland quarantine facility from the community, which includes 20 people who have tested positive for Covid-19 and their household contacts, the ministry said.
Three people are in hospital with Covid – one each at Auckland City, Middlemore and North Shore hospitals. All three patients are in isolation on a general ward.
"Since August 12, our contact tracing team has identified 3916 close contacts of cases, of which 3912 have been contacted and are self-isolating, and we are in the process of contacting the rest.
"Our total number of active cases is 71 - of those, 36 are imported cases in MIQ facilities, and 35 are community cases.
"Our total number of confirmed cases of Covid-19 is now 1464.
"Yesterday our laboratories processed 5417 tests, bringing the total number of tests completed to date to 910,853," the ministry said.