Prime Minister Jacinda Ardern and director-general of health Dr Ashley Bloomfield are making a plea to the remaining 367 people who left 14 days managed isolation after June 9 without a test to do their side of the deal and come forward.
"Do your bit," said Ardern. "Get back in contact. It's a small thing that you can do as a member of our team of five million."
Meanwhile, Deputy Prime Minister Winston Peters today outlined what he saw as the requirements to re-open New Zealand's borders for tourists and travellers.
If New Zealand was dealing solely with an Australian state such as Tasmania, we wouldn't need a vaccine, said Peters, but these moves were complicated by the federal state system.
"There are countries and populations - Queensland is one state and Tasmania is a second state, where we can get started. The Cooks, Niue, maybe other ones as well. But we need to be sure if anything went wrong there we had the facilities to deal with it."
For other, major countries the challenge was much bigger.
Countries would have to have a clean record, Peters told Newstalk ZB's Mike Hosking - zero community transmisson cases, like New Zealand has had since April 28.
"What they need is a clean record but the trouble is it's going haywire in those countries. A second spike in Beiijing. In the states, California, and Texas have seen a massive rise in the last 24 hours.
"If we don't get on top of this thing and get a vaccine, our chances of an economic recovery and worldwide recovery is seriously delayed.
"At this time, in July 2020, we surely have got the genuis, academic progress and the clinical capcity to do something about it. Very soon, I am very confident we are going to have the solution, but it's not here now."
New Zealand has joined a global initiative that aims to enable all countries to access a safe and effective Covid-19 vaccine, Peters announced yesterday.
The COVAX Facility was recently launched by Gavi, the Vaccine Alliance. The Alliance includes the World Health Organization, UNICEF, the World Bank and the Bill & Melinda Gates Foundation. It vaccinates millions of children worldwide for a range of diseases.
"We are out to see whether we can collectively find the vaccine," Peters told Hosking. "And to make sure that we don't see a competition for some countries that rules out other countries. Our job is to make sure we are at the right end of the queue."
Bloomfield said Friday would be the last day he would give daily reports on the numbers which were identified as having left isolation after June 9 without a test – the date on which day 3 and day 12 testing was supposed to have started.
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Of the 1359, most have been contacted and tested negative or referred for a test; 142 will not be tested including 84 who have refused a test; and 367 people have not responded to repeated contact, including 56 who have been referred to finding services for having an invalid phone number.
"We've gone to extra effort to make contact," said Bloomfield "And the next step is for people to keep their side of the deal."
Since April 9 arrivals have been required to go into managed isolation or stricter quarantine for suspected or confirmed cases and are now not allowed to leave without a negative test.
There were no new cases reported yesterday by the Ministry of Health, the second day in a row, meaning the number of active cases remained at 22.
They have all been caught in managed isolation or quarantine - with only one person in Auckland city hospital in a stable condition. There is no known community transmission.
Bloomfield said New Zealand would be watching the new outbreak in Melbourne where parts of the city comprising 300,000 have been put into lockdown for the next month.
"We have worked very closely with Australia and will continue to do so," he said. "We will watch the latest development closely to see how this approach and the measures they are putting in place such as localised lockdowns, play out."
The outbreak is thought to have been spread by security guards at a quarantine facility.
Air New Zealand has suspended flights to Melbourne for the time being.
Ardern said the fact the outbreak in Victoria happened from quarantine showed how "tricky" Covid-19 was.
"We will all battle this ongoing pandemic for some time to come, " she said.
"For all New Zealanders, it means remaining on guard."
National health spokesman Michael Woodhouse yesterday told Parliament that doctors were confused about changes to the Ministry of Health case definition for Covid-19.
He said he was aware of a GP practice in East Auckland which had referred 40 patients to a community-based assessment centre in Botany but only three had been tested and 37 had been turned away.
That was contrary to the previous message from the Prime Minister two months ago which was to get a test even you had a sniffle or a sore throat.
Woodhouse said he did not have an issue if the criteria for testing had narrowed.
But he said there needed to be clarity for doctors because there was a "disconnect between the reassuring rhetoric and what is actually happening."
Health Minister David Clark said the Government's position had not changed.
"If anyone has symptoms of Covid19, including a sniffle or sore throat, they should seek advice about a test from Healthline or their general practice."
People who had symptoms but were not considered a new higher index of suspicion would not be automatically required to self-isolate until the results came back, as they had been before.
Testing on Tuesday had totalled 4530, taking the total number of tests to 402,000.