More than 50 applications to leave managed isolation early on compassionate grounds could be approved next week, but under a much tighter process due to safety concerns.
Meanwhile Clutha-Southland MP Hamish Walker is rejecting accusations of racism after he raised concerns about Kiwis flying in from "India, Pakistan and Korea" and potentially heading to facilities in Queenstown or Dunedin.
Border measures remain the Government's focus because there is no local transmission of Covid-19, and all 18 active cases are in managed isolation or quarantine facilities.
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Yesterday there were two new cases of Covid-19.
The first new case is a man who arrived in New Zealand on June 27 from California. The second is a woman 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.
Cabinet Minister Megan Woods, who has ministerial oversight of quarantine and managed isolation facilities, said resuming compassionate leave would be prioritised next week - but only if it could be done safely.
There have been 57 applications waiting to be considered since a Government crackdown on June 16, when it emerged that two Covid-infected sisters who flew in from the UK had been granted leave without first being tested.
From June 9, early leave was not meant to be approved before there was a negative test, but that requirement wasn't followed for 52 out of 54 people whose leave was approved between June 9 and June 16.
Air Commodore Darryn Webb, who is in charge of the end-to-end border process, said he wanted a "low trust" model.
Previously people granted leave could, for example, drive themselves to a private home to see a dying loved one, and could then self-isolate for the remainder of their 14-day period.
But the lack of monitoring had been taken advantage of, with two people even running off after attending a funeral in Hamilton.
The new model could see Government control of travel services and a requirement to return to managed isolation. An escort could accompany those on leave to ensure compliance with all conditions.
The Government will also be aware of being successfully challenged in the High Court over compassionate leave, which had led to a loosening of the criteria.
Yesterday there were 5305 people in quarantine and managed isolation facilities, but that is expected to increase to 6481 next week.
The country's 24 quarantine and managed isolation facilities will be increased to 27 next week.
A facility in Hamilton will soon be ready, while Dunedin and Queenstown were also being looked at, Woods said.
That prompted a press release from National MP Hamish Walker saying it was "absolutely disgraceful" that southern communities hadn't been consulted.
"These people are possibly heading for Dunedin, Invercargill and Queenstown from India, Pakistan and Korea."
Woods said Walker's comments were "disgraceful and reprehensible".
"I think he's trying to stir up a sentiment that I don't think has any place in New Zealand."
But Walker told the Herald he was concerned about the high infection rates in those countries.
The ministry is still trying to contact 294 people who left a managed isolation facility between June 9 and 16 without being tested.
They were in isolation for two weeks, and have now been out for more than two weeks, so pose a very low risk.