Safe travel zones could be opened up between New Zealand and countries or areas with no community transmission, the Health Minister says.
Chris Hipkins told Morning Report talks are continuing to establish safe zones, which would allow quarantine-free travel.
"It is possible as we get through this, as we get to an extended period with no more community transmission, that those safe zones could open up."
Asked if Australian states would have to be able to show 28 days without community transmission, Hipkins said it was among the criteria, however, the re-opening of borders within Australia was a sticking point, "slowing down our eagerness".
"There are some states that we could have travel with relatively quickly but if there is a risk that they will then re-open their borders between states then obviously that increases the risk of there being transmission between states in Australia which therefore makes us a bit more hesitant.
"We are being very cautious around that."
If safe zones were operating, Auckland International Airport would effectively be split in two, to separate travellers from other countries and transit passengers who would not be able to use the safe zone flights.
A technical advisory group was still looking into the possibility of a third Covid-19 test for travellers arriving in New Zealand, Hipkins said. This could be done a week after their release from managed isolation to pick up a minority of people who cultivate the virus for more than 14 days.
He said now that the entire country is at alert level 1, he was urging people to continue to use the Covid-19 app which makes contact tracing much faster.
"If we remain vigilant we can keep our freedom for longer."
This time round he was confident there was stronger testing of people arriving in the country as well as better monitoring and testing of staff working at the border.
"One of the things that makes me a little nervous is we're heading into summer so we'll see fewer people with flu-like symptoms and of course that means fewer people getting tested.
"Those testing rates are our line of insurance, if you like, and we look to those that we make sure if anything is happening we're picking it up."
At the moment testing rates are around 4000-5000 daily and an average of 3000 to 4000 a day would be acceptable.
Regular testing of those working at border as well as those arriving will continue, some people will still get sick over summer, and GPs are being encouraged to test people who are showing symptoms.
'Risks aren't zero'
Covid-19 modeller Professor Shaun Hendy is warning the risk of a new surge of the coronavirus remains.
Auckland has now joined the rest of the country at alert level 1 and there are 37 cases in managed isolation, all of which came from overseas.
He told First Up keeping up testing will be key to avoiding future outbreaks.
"Every time we see a new way through we close that loophole but we have to acknowledge that the risks aren't zero and there's still the possibility of it making its way through those facilities."
However, the country is in "an amazing position" by eliminating community transmission again, especially when compared with many other parts of the world.
The outbreak that led to Auckland's shutdown had been harder to model than those back in March and April.
But he is pleased Aucklanders responded so well to a request for testing: "That helped us close this cluster off quickly."
Contact tracing had also functioned effectively.
Professor Hendy urged people to keep using the app and to be tested if they had any symptoms.