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Prime Minister Jacinda Ardern has left the door ajar to move the country into alert level 1 in less than four weeks.
But she and health chief Ashley Bloomfield are warning about the "long tail" of Covid-19 and the possibility of a second wave - especially as the limit on social gatherings increases to 100 from midday today.
Cabinet is set to look at whether New Zealand should move to level 1 on June 22, but pressure is mounting to move earlier, with Deputy Prime Minister Winston Peters saying it should have already happened.
Yesterday a top business restructuring expert, Grant Graham, whose firm KordaMentha partner makes money from insolvency work, pleaded for a move to level 1 to save "unjustifiable" job losses.
"Show us you believe in our recovery, don't wait for things that just aren't there. Announce level 1 immediately," he said in a social media post addressed to Ardern.
The developments come as the number of global cases is set to hit 6 million - they currently stand at 5.93 million. There have been 357,000 deaths around the world, including 101,000 in the United States.
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Yesterday was the sixth straight day of no new Covid-19 cases, and there have been no community transmission cases - whose branches are harder to trace and isolate - since the beginning of April.
Part of the Ministry of Health's elimination strategy is to have snuffed out "chains of transmission in our community for at least 28 days" - but it is unclear if this means 28 days of no new cases, or 28 days since the last community transmission case.
There are no Covid patients in hospital anymore, and with most infected people having recovered, there are only eight active cases.
It is possible that there will be no active cases in New Zealand by Cabinet's D-day on June 22.
Meanwhile Stats NZ revealed that the number of filled jobs plummeted by a record 37,500 in April.
The decimated industries of tourism, hospitality, and events are hoping for an earlier move to level 1, where there will be no physical distancing requirements and no restrictions on numbers at social gatherings.
The borders will still be tightly controlled, but Peters yesterday threw his weight behind Auckland Council's push for international students to return to New Zealand.
Peters said New Zealand could safely receive international students immediately - with an appropriate quarantine - and it should be given the greenlight "as fast as possible".
Ardern said on Monday that Cabinet would consider the settings of level 2 in 10 days, on June 8, and it will meet no later than on June 22 to look at whether the country could move to level 1.
She reiterated that timetable yesterday, saying it was based on Bloomfield's advice.
But Cabinet could decide, based on his advice, to open up level 2 even more after June 8, or consider moving to level 1 before June 22.
"We have given us some space, just in case," Ardern said yesterday.
"We are opening up much more rapidly than other countries, but we don't want to jeopardise the very privileged position New Zealanders have earned.
"They worked hard to get us here and I don't want to lose that."
She had been on a conference call on Wednesday evening with a number of countries' leaders who are considered to have fought Covid-19 well.
"All of us are really working hard to make sure as we ease restrictions - and many of those countries are still seeing 50 cases a day - we don't see second waves. That's on all of our minds."
Asked why level 2 was necessary for four more weeks, Bloomfield said Covid-19 had a "long tail".
A new outbreak triggered from a 100-person social gathering might not show up in testing data for weeks, which was why Bloomfield's advice was for at least two two-week incubation cycles at level 2.
"We have also seen some people testing positive quite a long way after they might have originally been infected," he added.
Peters said Bloomfield was an expert, but health was only part of the equation.
"Advice is one thing, but we have to make decisions about something else - the absolute crisis we've got with our economy.
"The faster we turn that around, the better."
A timetable for transtasman flights in July was being worked on, but Peters pushed for immediate flights to Australian states that had successfully contained Covid-19, such as Tasmania.
"Look at the Queensland results. Look at the Northern Territory results. They exceed ours.
"We've got to take all the expert advice into consideration. But be sure of this - all that medical advice is only so sound while we can pay for the outcome of this. And that's what I'm concerned about."
Bloomfield said that any community transmission in Australia would be a red flag.
Ardern said she and Australian Prime Minister Scott Morrison were "very, very keen" to open borders as soon as it was safe to do so.
September was "realistic", she said, but was cautious about putting a timeline on it.
Yesterday an elderly woman who died in Auckland last week became New Zealand's 22nd Covid-19 death.
Bloomfield said Hunter's death will now be treated as being related to Covid-19, following concerns from her family that she had contracted the virus during an outbreak that infected staff and patients.