The man in his 60s had underlying health conditions and contracted the disease from a close personal contact, with his death bringing the national toll to 99.

States and territories have been easing restrictions on indoor and outdoor gatherings and business, but border control remains tight.

NSW Premier Gladys Berejiklian has hit out at her Queensland counterpart Annastacia Palaszczuk who says her state's border with NSW may not reopen until September.

Ms Berejiklian said the sooner people could travel to other parts of Australia, the quicker the economy would recover.

Airline pilots sided with the NSW leader on Monday, urging a July 1 border reopening.

West Australian Premier Mark McGowan backed Queensland, saying his state's borders will remain closed until it's safe to reopen.

"We had very low rates of infection here, they had higher rates in the eastern states, so we will keep the border up until we think it is the right time for the health of Western Australians," he told reporters in Perth.

South Australian Premier Steve Marshall has also backed Queensland and Tasmania on tight border controls, saying a quick reopening would compromise efforts already made.

"I think there will be a time when we open up the borders but it's not now," he said.

Tourism minister Simon Birmingham urged the states to lift their borders.

"I expect that if the successful suppression of COVID continues then the states should be relaxing their border controls," Senator Birmingham told Sky News.

"If one or two states were to hold out they will be answerable to their tourism industry and will need to provide additional support to that industry."

Deputy chief medical officer Paul Kelly says that while it's up to the states to make decisions, they were never advised to close their borders.

"We didn't see a reason to close them in the first place," he told reporters in Canberra.

Professor Kelly says more than 5.6 million people have undertaken a telehealth consultation, leading to $526 million for doctors.

Despite only nine cases being reported nationally on Monday, concerns continue about the spread of the virus.

McDonald's has closed 12 outlets across Melbourne after a delivery driver tested positive to the disease.

The driver was an extended family member of a worker at Fawkner McDonald's in the city's north, where a cluster of 10 cases emerged earlier in the month.

A Domino's outlet has been shut for cleaning after a worker contracted the virus, while the abattoir linked to 99 cases is beginning to reopen.

The Victorian government has announced a $2.7 billion in road and rail upgrades to kickstart the state's economy.

Australia's push for an inquiry into the origins of coronavirus is gathering international momentum, with more than 110 countries co-sponsoring a World Health Assembly motion.

The motion is due to be voted on in the early hours of Tuesday morning.

China has been furious with Australia over the inquiry, which now has the support of Russia, the European Union, India, Japan, Canada and Britain.

More than 7000 people have contracted coronavirus across Australia, with 6367 already recovered.

Australian Associated Press