Deputy Prime Minister Winston Peters says there are "aspects" that could point to the opening of a trans-Tasman bubble under Alert Level 2.
Prime Minister Jacinda Ardern tomorrow will join Australia's Cabinet meeting to discuss the possibility, but warned it would not be in the "very near short term".
Mr Peters also told TVNZ1's Q+A with Jack Tame that travel between regions could be a possibility under Alert Level 2.
"If it's to actually have the effect of reopening up our economy, travel between regions will be essential," he said.
According to the Covid-19 website, people are advised to minimise non-essential travel under Alert Level 2. Under Alert Level 3 travel between regions is limited to selected reasons such as essential work or medical and compassionate reasons.
When asked if he would support domestic tourism under Alert Level 2, Mr Peters said "most certainly, it's mass gatherings which are the concern".
"If we can and we should be able to with the airlines and a number of other transport utilities, practice safe movement and safe assembly then we will facilitate economic recovery doing that."
"If we don't and we haven't got it ready, we should be working around the clock 24/7 for the day when we open up."
On the trans-Tasman bubble, Mr Peters said there was aspects that meant it was "surely possible".
He gave the example of bringing Australians to New Zealand to use the ski fields, while "managed in very close circumstances".
Moves in Australia to tighten the rules around proposed foreign investors, subjecting them all the be scruitinised by the Foreign Investment Review Board was the "right move", Mr Peters said in the interview.
He added he and others were pushing "real hard, as fast as possible" to go in the same direction.