The total of confirmed and probable cases in New Zealand is now 368, with 30 of those described as probable and 37 already recovered. Recovery is defined as being symptom-free for 14 days.
Bloomfield said the number of people with the disease was expected to start to level off in roughly 10 days' time.
He again called on anyone who was waiting to hear back about a test to stay in self-isolation.
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The capacity for testing was now 2000 per day. That was on a par with Germany on a per capita basis, Bloomfield said.
A strong link to overseas travel was still being seen in New Zealand cases, he said.
Northland's third confirmed case was a female in her 50s who left the UK on flight EK38 to Dubai on March 19. She took flight EK448 to Auckland, arriving on March 21.
No further detail is known as yet about the fourth case.
New Zealand entered its second day of lockdown today.
• Covid19.govt.nz: The Government's official Covid-19 advisory website