The current social distancing rules and closures would remain in place for four weeks, when they would be reviewed, Mr Morrison said, paving the way for an earlier-than-expected easing up.

He also foreshadowed the possibility that elective surgery would begin again as early as next week after leaders meet again on Tuesday, and he said parliament would return for a test run of normal business in May.

He was speaking as the government released new modelling showing Australia as a world leader in detecting symptomatic coronavirus cases, with an estimated 93 per cent of people with symptoms being picked up.

But the Doherty Institute, which did the modelling, also pointed out that the number of undetected "asymptomatic" cases, including those with mild symptoms, might be high. Overseas estimates suggest that anywhere between 40 and 80 per cent of all infections remain undetected.

Mr Morrison said authorities would use the next four weeks to establish more extensive testing, not only of people with coronavirus symptoms.

Contact tracing would also be beefed up.

The states and territories had "a team of Sherlock Holmeses out there at the moment". But, "we need to lift that to an industrial capability and do that using technology and we need to do that as soon as we possibly can", he said.

Australia has 6468 cases, with 63 deaths. On Thursday, 42 people were on ventilators.

There were just 21 new cases in the 24 hours to 3pm on Thursday, with authorities urging more people to front up for testing.

Chief medical officer Brendan Murphy said the numbers were encouraging but relaxing distancing measures would mean more outbreaks.

"Unless we are prepared as a nation to detect those outbreaks really early and get on top of them and control them and isolate the cases and quarantine the contacts, we could end up with large community outbreaks that could lead to situations like we've all seen every night on the nightly news in high-income countries with good health systems like the USA and the UK," he said.

"We can't afford to do relaxation until we have a public health system which is so finely tuned that it can detect and respond to any outbreak."

The Doherty Institute has used a new model developed by the London School of Hygiene and Tropical Medicine, which suggests Australia is detecting about 93 per cent of cases where people have symptoms.

All of the states are likely to be detecting more than 80 per cent of cases - at the lower end in the ACT and the higher end in NSW, Queensland and South Australia. The rate is well above other countries.

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Analysis by the Actuaries Institute this week suggests cases could be six to seven times higher than the official figures, with as many as 20,000 carriers in Australia.

But Professor Murphy said while he could not be sure, the number was probably too high.

"It's pretty clear now there are some asymptomatic cases of COVID-19 that don't present for testing, but we have done some pretty broad scale testing," he said.

"If we had that level of undetected cases we would have found it by now but we're definitely broadening our testing and surveillance."

The Doherty Institute urges caution.

Director of Epidemiology Professor Jodie McVernon said at Australia's current transmission rate, every 10 infected people were passing the virus on to just five others, which was good news.

"It doesn't let us be complacent," she said. "The virus hasn't changed. It still has the same characteristics. And if we were to release those measures now, knowing that one case on average ... produces another two and a half cases, 10 cases today would produce 25 cases over the course of the infection, not five."

Physical distancing and reduced group sizes were set to remain part of the Australian landscape.

"Life as normal is not a real option because the virus will come back from somewhere," she said.

Professor McVernon estimated that anywhere between 40 and 60 or even 80 per cent of people with coronavirus might be undetected - because people have no symptoms, mild symptoms, choose not to present or could not be tested.

Antibody testing is likely to give a clearer picture, but antibody testing was "still a work in progress and not widely available", with the World Health Organisation now looking to evaluate different tests, and provide recommendations to countries on which ones are the best to use in different types of studies of immunity - such as tracking antibody levels in individuals over time, or to providing snapshots of immunity across whole populations.

Professor of Mathematical Biology Professor James McCaw said the potentially high number of undetected cases "definitely makes you very cautious about relaxing measures".

The national cabinet agreed on Thursday that mobile phone apps should be "wholly explored" to track contacts.

Restrictions would not be wound back without an assurance that the system would cope with any surge in cases, including the requirement for hospital beds, ventilators, protective equipment and staff, and until supply lines for equipment were assured.

While New Zealand is bent on an "elimination" strategy, the national cabinet is describing its strategy as "suppression/elimination".

Mr Morrison said that was the best path, given Australia's love of freedoms and the economic trade-off.

"The eradication pathway involves an approach which will see even more economic restrictions than are currently in place and that is not seen to be in our view a wise trade-off in how we are managing the two crises that we are facing, the economic one and of course the health one," he said.

"We are doing well on the health one and I want to do that on the economic one."

The restrictions were "rubbing at the edges a bit in parts of the country and that is understandable", he said.

"We like our freedoms, we like to be able to do what we want to do. We like having a barbecue, we like going out and we really miss it and we miss our kids being able to get together and go to school and be with their friends, we miss all of them. The suppression path is the best Australian path."

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