PM Jacinda Ardern says New Zealand can take heart from there being no new coronavirus cases today. But she says it reflects the success of the lockdown rather than actions during level three.
A transtasman bubble with certain Australian states could open up even before interstate border bans are lifted.
Australia's Federal Tourism Minister Simon Birmingham said New Zealand was the first choice for an international travel bubble, the Sydney Morning Herald reported.
"New Zealand is obviously the first, and right now only,international market that we could safely agree to open up to," he told the Age and the Sydney Morning Herald.
"If New Zealand and some Australian states are ready and willing to progress, then the reluctance of other states to open up their domestic borders shouldn't become an obstacle to progress."
He said such travel should not rely on other states, such as Queensland, keeping their borders closed.
"The recovery of jobs and small businesses in some states shouldn't be held back by the decisions of other state governments."
Queensland's local government earlier this month released a "roadmap to easing restrictions", setting out expected dates certain restrictions would lift or be adjusted.