Hamilton will soon be ready to quarantine returning Kiwis and Dunedin and Queenstown are also being looked as centres where people can isolate.
Cabinet Minister Megan Woods and Air Commodore Darryn Webb are giving a press conference on the Government's Covid-19 response.
On Health Minister David Clark's resignation and whether she had been distracted by him, Woods said they had worked constructively together.
There are 24 quarantine and managed isolation facilities right now, which will be increased to 27 next week, Webb said.
Asked about any bad behaviour at the facilities, Webb said he had seen no evidence of drug dealers and prostitutes going into quarantine and managed isolation facilities.
He said there was no guarantee a foolproof system. "It's a human system. We are setting up as robust a system as we possibly can."
Woods added that people couldn't just wander into the facilities they have visited.
There were 815 day three and day 12 tests completed yesterday, which was more than the planned 785 tests.
Webb said there are 5305 in quarantine and managed isolation facilities, and current capacity was 6058.
Next week the number expected in quarantine and managed isolation facilities is 6481, while the capacity will be 6774.
More Defence Force and government personnel were also being brought on to shore up the end-to-end system.
Next week the priority will be to reinstate compassionate exemptions, Woods said.
"It is our absolute priority to ensure these can safely go ahead."
Woods said the criteria for compassionate leave was being reviewed, including how long someone needs to be in a facility and whether they need a negative test before leave could be granted.
Whether someone granted leave could self-isolate in the community after leaving for the remainder of the 14-day period was something still being considered, she said.
"These are exemptions. There are about exceptional circumstances."
There are also more people in facilities, and safety would be the chief priority in any compassionate leave.
Woods said daily information sheets will be available, including how many are in quarantine and managed isolation facilities, and the inflow and outflow of people, as well as testing data.
Samples from hotels will also be fast-tracked, particularly for day 12 tests, she said.
Wastewater will be sampled at the Jetpark Hotel from next week as well.
False alarm at Jetpark
Webb said this morning, at 935am, a fire alarm went off in at Jetpark Hotel in Auckland where returning Kiwis are in quarantine.
Those inside were safely evacuated and were also kept physically distant from each other.
He said it was a false alarm and there was no fire.
Webb said he would be surprised if people were still arriving at quarantine and managed isolation facilities without knowing about the mandatory 14-day stay.
The Ministry of Health announced two new cases of Covid-19 today, but there are still no cases in the community.
With six cases recently recovered, the number of active cases is 18 - all contained in managed isolation or quarantine facilities.
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The first new case is a man in his 30s who arrived in New Zealand on June 27 from California.
The second case is a woman in her 30s who arrived on June 21 from Kenya, via Doha and Brisbane. She is the wife of a previously reported case.
One person remains in Auckland City Hospital in a stable condition on a ward.
With no community transmission, the focus in the fight against Covid-19 is on keeping any imported cases from overseas contained in facilities and preventing any spread into the community.
The ministry is still trying to contact 294 people who left a managed isolation facility between June 9 and 16 without being tested.
People in this group were in isolation facilities for two weeks, and have now been out of isolation for more than two weeks, so they pose a very low risk.
This morning Clark resigned as Health Minister because he had become too much of a distraction to the Government's work.
He offered his resignation to Prime Minister Jacinda Ardern in person last week, and she accepted it.
Clark will still stand in September's election in his seat of Dunedin North, and while Ardern has left the door open for his possible return to Cabinet if Labour win the election, she said he would not be Health Minister.