Two siblings of the latest Covid-19 case from Papatoetoe High School have also tested positive.
Earlier today, the Ministry of Health said a teenager considered to be a casual-plus contact of the community cases had tested positive.
The Papatoetoe High School student had not returned to school on Monday when it reopened, Minister of Covid-19 Response Chris Hipkins said.
The new cases are the siblings of today's case - a teenager and an infant. The parents and a third older sibling have returned negative tests so far, the ministry said in a statement.
The family has been transferred to the Auckland quarantine facility.
The teenage sibling recently finished school and has been working at Kmart Botany. They were at work on Friday 19 February and Saturday 20 February between 4pm and 10pm.
The ministry said it is now a location of interest and anyone who was there at those times is considered a casual plus contact.
If you are a casual plus contact, you are advised to immediately isolate at home and call Healthline on 0800 358 5453 for advice on isolation timeframes and testing requirements.
Thirty-one staff at Kmart have already been identified as close contacts and are isolating and being provided with public health advice.
Dark Vapes at East Tamaki has also been identified as a location of interest, with a visit on 19 February between 2.30pm and 4pm, and 20 February, between 7pm and 8.30pm.
The up to date locations of interest can be found here.
On the ministry's website, the advice is for casual plus contacts of these locations to isolate at home for 14 days from date of exposure, have tests at day five and day 12 after exposure, call Healthline 0800 358 5453.
The ministry said more locations of interest for today's cases were being investigated. The infant does not have childcare outside the home.
A testing centre was set up at the school this afternoon and 672 tests were done today.
Testing will be available again at the school tomorrow for those who were unable to receive it today.
The ministry is advising everyone in a Papatoetoe High School household must stay away from work or any other school, educational facility or community setting (e.g. the supermarket or any other place outside the home).
The school remains closed and no students or staff will be able to return until advised by a Medical Officer of Health.
At this point, household members who are not students or staff do not need to be retested, unless they have symptoms or are asked to do so.
Further updates on contact tracing and genome sequencing of today's earlier reported case would be available tomorrow, the ministry said.