In what could be a major breakthrough, only one of the 12 cases detected nationally between Monday and Tuesday morning was unable to be traced.

Health Minister Greg Hunt said it was the most important figure he had seen in dealing with the virus.

"It means that as a country we are not just flattening the curve but we are consolidating it, extending it and securing it," he told reporters on Tuesday.

Australia's coronavirus death toll is at 88 after four more victims lost their lives at western Sydney nursing home Newmarch House, where 11 have now died.

The federal government is warning aged care providers not to isolate residents from visitors beyond health guidelines.

Aged Care Minister Richard Colbeck said facilities could apply for exemptions if there were outbreaks.

"We're not talking about going back to open slather visitation," he told the ABC.

Australia is maintaining a low rate of new cases, with 6731 people diagnosed with the disease, more than 5600 of whom have recovered.

There are 113 people in hospital, with 43 in intensive care.

Coronavirus restrictions are increasingly different across state borders as premiers balance infection risks against economic and social pain.

NSW will from Friday allow two adults to visit another house for any reason, regardless of how many people live there.

But Premier Gladys Berejiklian has warned of more infections as social interactions increase.

"This isn't a licence to go wild and to have massive parties," she said.

NSW is also pushing ahead with plans for students to return to classrooms from May 11.

In contrast, Victoria is refusing to loosen restrictions, with parents being encouraged to keep children at home where possible.

Premier Daniel Andrews says he's happy to cop criticism for being too cautious given what's at stake.

"These numbers are exactly the sorts of numbers that we wanted to see. But it is fragile and it can change very quickly," he said.

Queenslanders will be permitted to travel up to 50 kilometres from home for picnics, visiting parks or non-essential shopping.

Students are also learning from home in large numbers in that state, with the direction to keep children at home where possible due to be reviewed on May 15.

West Australian schools are set to reopen on Wednesday, while up to 10 people can now gather for non-contact recreation in the state.

South Australia hasn't flagged when it will ease its rules, which are less restrictive than other states, while the NT is looking at when pubs might reopen.

Tasmanian Premier Peter Gutwein is hopeful of lifting some restrictions in the state's northwest on Sunday after an outbreak triggered a strict shutdown.

Mr Hunt said Australia was the envy of the world because of its success in stopping the spread of coronavirus.

"Every restriction that is lifted is a cause for celebration," the health minister said.

On Tuesday afternoon, more than 2.4 million people had downloaded the new COVIDSafe contact tracing app.

Treasury secretary Steven Kennedy said businesses would close permanently after the crisis as he outlined the unprecedented speed of the economic shock.

The economy could be dealt an incredible blow if China follows through on a consumer boycott threat.

Senior ministers have pushed back against the inflammatory comments from the Chinese ambassador, who received a call from the foreign affairs department.

Australian Associated Press