Dr Bloomfield said 89 new cases bringing New Zealand's total to 1039.
He said there were now 12 clusters, an increase of two from yesterday. Clusters are defined as 10 or more infections from the same place.
The Marist College cluster had 66 cases and was the largest in New Zealand.
He clarified that people who had returned from overseas needed to be considered as close contacts, and needed to be isolating themselves even from members of their own family.
He said they should not be accessing essential services.
Prime Minister Jacinda Ardern says New Zealand has had a relatively steady increase in cases compared with the numbers seen overseas.
"Our case rate and death toll is well below other comparable countries. Yes, we had the benefit of time because our distance and because our early border and mass gathering measures also made a difference there."
"Going hard and going early appears though to be going well for us."
She said New Zealanders should be proud of the difference they had made, and urged them not to let up.
"This is why we have strengthened efforts to go after those who aren't sharing that mission and who appear to be breaking the rules."
"While compliance has been generally strong, there are still some I would charitably describe as idiots."
Ardern referred specifically to a man who filmed himself coughing on people at a Christchurch supermarket.
She said the government's focus this week remained on stopping the virus so the lockdown could be lifted.
Ardern also said there had been no decision to extend the lockdown.
She said there were no plans for any kind of Level 5, as "this is as tight as it gets".
She said some regions may stay under lockdown longer depending on the situation there, and New Zealanders should continue to maintain the measures even once the country was believed to be past its peak.
Dr Bloomfield yesterday said 82 new cases had brought the total in New Zealand to 950, with 10 in hospitals including one in intensive care. One person has died.
The Ministry of Health yesterday also clarified some of the rules during the lockdown, including on forms of exercise.
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