The nation's largest city was put into a three-day lockdown on Sunday after three unexplained cases were found in the community. It was the first lockdown in six months in a nation which so far has managed to successfully stamp out the spread of the disease.
The original cases from the latest outbreak were a mother, a father, and their daughter, who attends high school. Health authorities said the two new cases were a high school classmate, who was a close contact of the daughter, and the classmate's sibling.
However, ramped-up testing has not indicated the virus has spread further. Laboratories processed more than 17,000 individual tests on Tuesday, authorities said, and they also tested wastewater samples which came back negative.
Senior lawmakers in the Cabinet are meeting Wednesday afternoon to decide whether to extend the Auckland lockdown and the heightened restrictions that have been imposed on other parts of the country.
Prime Minister Jacinda Ardern said the Cabinet would take into account the fact that the classmate had already been identified as a close contact of the daughter and had been asked to isolate along with other close contacts.
She said that among close contacts “obviously then it's not surprising to us if we get a positive test result."
Many New Zealanders had been hopeful the lockdown would be short-lived after no new cases were found on Monday or Tuesday.
Genome testing has shown the family caught the more contagious variant first found in Britain.
The mother who caught the disease works at a catering company that does laundry for airlines. Officials have been investigating whether there is any link to infected passengers, but so far haven't been able to find a direct connection or explain how the outbreak might have begun.