Director-General of Health Ashley Bloomfield says the 13 new cases are all linked to one Auckland cluster - the four people who were reported as confirmed cases yesterday and the day before.
He says the one new case in managed isolation is a woman in her 30s who arrived from the Philippines.
There are now a total of 36 active cases in New Zealand.
Dr Bloomfield says 17 of these are linked to the new outbreak: "Given that all these cases are linked, we are treating them as a cluster."
Dr Bloomfield says that one of the new cases is a student at Mt Albert Grammar School, as was made public this morning.
"The student was not symptomatic while at school and has not been at school since they became unwell and got tested so the chance of exposure ... is low at this point."
Dr Bloomfield has confirmed that three of the people who have tested positive are workers at Americold, and seven are family members of the initial cases.
One person who has tested positive is an employee of Finance Now, and another person who has tested positive is their family member. There is also one new probable case in the community, which is also linked to the outbreak.
One of the people who tested positive visited an aged care facility in Waikato. Anyone who has visited recently will be notified.
Dr Bloomfield is not naming the facility yet as residents there are still being notified.
Discussing the family who had COVID-19 and went to Rotorua, he says the family checked in to Wai Ora Lakeside hotel at 3.30pm on 8 August. They visited the Herbs and Spice Thai restaurant at 7.30pm that day.
On 9 August they visited Fat Dog Cafe at 1.30pm and Pak'nSave at 3.30pm. At 3pm they went to the Heritage Farm and 3D Art Gallery, then Skyline Gondola and Luge about 4pm.
On the 10th, the Monday, the made a day trip to Taupō and made a boat trip. All the people on the boat trip have been identified and contacted.
Then they returned to the Heritage Farm and Art gallery, before visiting Burger Fuel at the Redwood Centre, and Don Kebab, about 7pm.
He says all new positive cases will now be treated in quarantine facilities.
"It will help us avoid any further inadvertent spread."
Dr Bloomfield reminded people that "there is no blame or shame in having COVID-19. The virus is the problem, not the people."
Laboratories processed 6006 tests yesterday. Dr Bloomfield says the total swabs collected yesterday was well over 10,000 but because the cutoff time for reporting is midnight not all of the results have been included.
Two more pop-up testing sites have been stood up in Henderson and Airport Oaks.
The testing centres in Rotorua and Taupō have extended their hours.
Dr Bloomfield says testing is available to any businesses that request it.
He says for the first time this morning the Ministry of Health has used the alert function on the NZ Covid Tracer app.
He says another 338,000 people have registered on the app.
GSR is continuing to lead efforts on genome sequencing.
"What we do know is that the pattern of the genome sequencing of the new cases most closely resembles the cases in the UK and Australia."