Director-General of Health Ashley Bloomfield says there have been no new cases of Covid-19 after a ramping up of testing in the past day.
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The number of active cases remains at three.
Dr Bloomfield said there were 6273 tests carried out yesterday and the higher number reflected testing in the community and extensive testing of people in the wide net of the latest cases and isolation.
"In that context, it is very reassuring that we have no further cases of Covid-19 to report."
He said New Zealand had capacity to do more than 12,000 tests in a day if necessary.
Two more significant clusters - the Rosewood rest home and the Bluff clusters - had now been closed and there was just one significant cluster - the St Margarets rest home cluster in Auckland - remaining.
Dr Bloomfield said between 9 June and 16 June, 55 people were granted leave on compassionate grounds. The vast majority have been tested and returned a negative result.
"It's important to emphasise that anyone who departs a facility on compassionate grounds does so under a very strict set of criteria."
He said the Ministry of Health was following up with 401 people in regards to the two women who tested positive on 16 June after travelling to Wellington, and 174 of them had returned negative results.
"The results of testing are very reassuring."
Dr Bloomfield said there had been 37 positive cases coming across the border since April.
Yesterday New Zealand recorded one new case of Covid-19, of a man in his 60s who is in quarantine after arriving from Pakistan, which brought the number of confirmed and probable cases to 1507.
The man had arrived on Air NZ flight 124 from Melbourne on 13 June, showed symptoms on 15 June and was swabbed the next day. He is staying at the Jet Park Hotel, and was transferred there with his travelling companion after developing symptoms.
The government bolstered its quarantine procedures after two women were allowed to leave quarantine without being tested and later were found to be infected.
Former RNZ reporter Alexa Cook, who is in quarantine at the Novotel Auckland Airport, having arrived from the UK, said the facility was being managed very strictly and nothing seemed to have changed.
But she said she was finally tested on day five, rather than day three, and had asked several times to be tested. The government said those in managed isolation and quarantine would be tested on day three and day 12 of managed isolation.