But Australians are being warned restrictions to contain the virus will be in place for many more weeks, while international travel is out of the question for the foreseeable future.

"It's unrealistic to think those border restrictions will be lifted anytime soon," Treasurer Josh Frydenberg told reporters on Tuesday.

Health authorities say the pandemic is moving into a containment phase.

They want to keep a close eye on possible community transmissions, where new diagnoses aren't linked to known cases or people who have brought the virus back from overseas.

Thousands more Australians will be checked for coronavirus as states expand their testing regimes to stop any spread among the wider community.

Deputy chief medical officer Paul Kelly said the official number of cases related to people diagnosed in lab tests.

"How many people have asymptomatic disease, or indeed are exposed to the virus and develop immunity without any symptoms at all, or have a mild case of the disease and never have gone to get their test done?" he told reporters.

"These are a mystery to us at the moment."

Testing regimes are being expanded across various states and territories to ensure more people showing symptoms - fever, shortness of breath, cough or sore throat - can be screened for the disease.

Some 6400 Australians have caught the virus and more than half of them have recovered.

There have been 62 deaths.

A cluster of cases in north-western Tasmania has led to two hospitals being closed and 5000 people put in quarantine.

Police are now investigating rumours some of the medical staff involved had met for a dinner party in breach of social distancing rules.

State and federal leaders will meet later this week to discuss when restrictions on travel and gatherings of people can be relaxed.

"I do want to caution Australians that we're not in that phase yet ... we're many weeks away from being in a place like that," Prime Minister Scott Morrison told Seven's Sunrise.

Any lifting of restrictions would need to be backed up by a strong health system and even stronger testing regime.

Prof Kelly said the leaders would be given a range of options.

Any easing of restrictions would have to be underpinned by having health systems ready to deal with a large outbreak of the virus just in case.

"We definitely don't want to just open up everything that we've dampened down on so far because we've seen in other countries what has happened with an uncontrolled epidemic and we just cannot afford to do that in Australia," Prof Kelly said.

He again emphasised the broad measures to damp down the virus would likely need to be in place for six months, until about September.

Chief medical officer Brendan Murphy has suggested digital tracking via mobile phones, as used in Singapore and Taiwan, could replace the tough restrictions

But he acknowledged there would have to be community buy-in for such a move.

Treasury modelling shows Australia's unemployment rate is expected to nearly double to 10 per cent because of the pandemic.

It was slated to reach as high as 15 per cent without government support.

Mr Frydenberg said the dramatic rise in unemployment was concerning but also a realistic reflection of the economic challenges ahead.

"As for the speed in which people get back into the workforce, who have tragically lost their jobs, that will depend, to some extent, the health restrictions are in place," he said.

He recognised the hundreds of billions of dollars the government was spending would leave the nation with "a debt burden that will be left to pay for years to come".

Australian Associated Press