"We will remain responsive to the health situation as it develops."
Morrison said it was good to have Ardern join their Cabinet meeting and the primary purpose was for her to share New Zealand's response to the virus with his colleagues.
He said the pair had been talking about the trans-Tasman bubble "for several" weeks.
The obvious start to connecting Australia with the rest of the world was to start with New Zealand, Morrison said.
The private sector and other stakeholders had expressed interest in the arrangement and officials would work closely with those groups, including the Australia New Zealand Leadership Forum.
But the trans-Tasman bubble would need to take into account state and territorial movement restrictions. There are currently bans on travelling between some states in Australia.
"A trans-Tasman Covid-safe travel zone would be mutually beneficial, assisting our trade and economic recovery, helping kick-start the tourism and transport sectors, enhancing sporting contacts, and reuniting families and friends.
"We need to be cautious as we progress this initiative. Neither country wants to see the virus rebound so it's essential any such travel zone is safe. Relaxing travel restrictions at an appropriate time will clearly benefit both countries and demonstrates why getting on top of the virus early is the best strategy for economic recovery," the prime ministers said.
The prime ministers said they'd worked together on Australia's and New Zealand's respective border settings since the Covid-19 pandemic began as each country had allowed the other's citizens to transit on their way home.
The work on the trans-Tasman Covid-safe travel zone reflected Australia and New Zealand's special relationship, the Single Economic Market agenda and the long history of freedom of movement between the two countries, the leaders said.
"Our relationship is one of family – and our unique travel arrangement means we have a head-start for when it is time to get trans-Tasman travel flowing again."
Once the travel arrangements across the Tasman were established, they would then look to include other Pacific countries which were interested in joining.
Morrison told media the arrangement was "still some time away".
Ardern was invited by Morrison to the meeting, which included the Premiers and chief ministers of all states and territories. The last New Zealand prime minister to join was Peter Fraser during World War II.
Australia has now recorded more than 6800 cases of Covid-19, with 3035 in New South Wales, 1423 in Victoria, 1043 in Queensland, 438 in South Australia, 551 in Western Australia, 223 in Tasmania, 107 in the Australian Capital Territory and 29 in the Northern Territory.
The death toll stands at 96.
READ MORE:
• Covid 19 coronavirus: Zero new cases for second day in a row
• Covid 19 coronavirus: Tenant booted out of home during lockdown following Tenancy Tribunal order
• Covid 19 coronavirus: Jacinda Ardern's warning despite zero cases, Ashley Bloomfield defends Ministry of Health on Mike Hosking show - 'we do have a heart'
• Coronavirus Covid 19: Zero new cases today - Ashley Bloomfield
Minister of Foreign Affairs Winston Peters said the Australasian population had to see itself "as one" with a system united in the attack on Covid-19.
Peters wanted it to be treated as a matter of "critical urgency".
Fifty-five per cent of New Zealand's tourists were Australians while New Zealanders were the second-largest group of tourists in Australia.
"We've got a lot at stake here so we've got to think outside the square and think as one ANZAC nation."
If both countries had the same technology, utilities and "had that confidence" the bubble could go ahead.
Asked whether he's like to see the transtasman bubble by the start of the ski season, Peters said:
"Urgency is everything at the moment. I know we've got to defeat Covid-19 but at the same time we've got to get this economy turned around and with the greatest of speed. Every day of delay is a day of setback."
Peters wanted a public-private sector taskforce to work on the transtasman bubble.