The 13th cases was from a managed isolation facility, reports Xinhua news agency.
The 13 new cases brought the total number of confirmed COVID-19 cases in New Zealand to 1,271.
The case from the managed isolation is a child returning New Zealand from Afghanistan via Dubai on August 3.
From early investigation, the 12 cases in the community were linked to the current identified cluster as close contacts of previously confirmed cases, said Bloomfield.
The public were urged by Health Minister Chris Hipkins to take tests only when they were symptomatic to avoid delays.
Hipkins also urged the public to be cautious about rumours and misinformation on the social media as one particular rumor was shared widely overnight in the community, causing online bully and damage to the family involved.
People were also encouraged to download official COVID-19 contact tracing app.
New Zealand businesses were asked to display contact tracing QR code for people to scan and register.
On Friday, Prime Minister Jacinda Ardern declared the Alert Level 3 lockdown for Auckland region and Alert level 2 restriction for the rest of the country to continue for 12 days until August 26.
New Zealand went to a month-long national Alert Level 4 lockdown in late March, and declared an early success of the COVID-19 battle in June.