Director-general of health Ashley Bloomfield says New Zealand has no new Covid-19 cases.
There were 6273 tests completed yesterday and a total of 327,460 total tests.
The tests were on community members and people in managed isolation.
At least 700 further tests were being carried out today, Bloomfield said.
Those considered contacts of New Zealand's three recent Covid-19 cases were also being chased up and tested, Bloomfield said.
Despite the big day of testing, no one had yet returned a positive result.
"In that context, it is very reassuring that we have no further cases of Covid-19 to report," Bloomfield said.
Bloomfield also made it clear that from now on, no one would leave managed isolation or quarantine early without returning a negative Covid-19 test result.
However, that had not been the case up until now.
Since managed isolation and quarantine facilities started in April, more than 19,000 people had passed through them, said Bloomfield.
He said the key measure to ensuring public safety was making sure every person self-isolated for 14 days.
Authorities had been ensuring this took place even in cases of compassionate exemption, he said.
Now that measure had been strengthened by adding routine testing, he said.
New Zealand now has three active cases of Covid-19.
They included two sisters from the UK, who were given a compassionate exemption to leave a managed isolation facility and travel from Auckland to Wellington by car.
The women were not tested before leaving managed self-isolation. But their subsequent positive test results on June 16 ended New Zealand's 24-day streak of no active cases.
The third case was of a man in his 60s who arrived from Pakistan via connecting flights through Qatar and Australia.
Yesterday, a man in quarantine at the border tested positive for Covid-19 after arriving from Pakistan via Doha and Melbourne on June 13 on Air NZ flight 124.
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Three people on the flight with the man from Pakistan had earlier been granted compassionate exemptions to leave managed isolation without tests.
They were now being chased up for tests, Bloomfield said.
Bloomfield said 401 people were considered potential contacts of the two UK sisters and were now being tested.
He said everyone who had been given passes out of managed isolation on compassionate grounds was being called back for Covid-19 tests.
Since the beginning of April, there have been 37 positive cases of Covid-19 of people in isolation or quarantine.
These tests were only undertaken on people who had shown symptoms of the virus.
Bloomfield said acknowledged people arriving in New Zealand were able to refuse a Covid-19 test.
However, authorities now had the power to hold anyone who refuses a test for up to 28 days - or two cycles of self-isolation.
He said the 6273 tests conducted yesterday enabled health officials to be sure they were ring fencing possible infections from the two UK sisters.
The current return of negative results gave authorities growing confidence the women had not caused widespread community infection.
When asked if the ministry could put a number to the people who have left an isolation facility without a test, Bloomfield said he could not yet do so.
His team would first chase up and test everyone deemed contacts of New Zealand's three recent cases.
Then they would work back to count how many people had been let out of managed isolation without tests in April and May.
However, he said all those people would have completed their 14 days' isolation.
Bloomfield said he had taken responsibility for not putting all the appropriate processes in place to keep New Zealand safe.
There was no longer any confusion about testing. Since Tuesday he had made it clear no one would leave a managed isolation facility before 14 days without a negative Covid-19 test result, he said.
New flight rules
Yesterday Bloomfield said the Ministry of Health would now require passengers to wear masks on flights from Australia.
This was because many people flew through Australia from other countries and all of the three latest cases had come via Australia.
And Air New Zealand crew flying long-haul international flights, such as to the United States, are now required to self-isolate at home and return negative tests before being allowed into the community.
Air crew on other long-haul international flights already have "very strict" protocols in place, including not going "land-side", said Bloomfield.
Former RNZ reporter Alexa Cook is in quarantine at the Novotel Auckland Airport, having arrived from the UK and was on the same flight as the man who tested positive yesterday, a week ago.
She said at the time there was no social distancing or masks and that concerned her.
"We were sat in the middle of a row of four people - we had people right up against us," she told RNZ.
"Masks were not compulsory, the flight attendants were only wearing a mask and no other PPE ... and the flight itself seemed to be very crammed, very busy."