Victoria state, home to a quarter of Australia's 25 million population, recorded 55 new COVID-19 cases in the 24 hours to Tuesday morning. That was up from the previous day's 41 new cases but far below a record daily increase of 725 a month ago.

The Victoria outbreak - it now accounts for about 75% of Australia's nearly 26,400 cases and 90% of its 770 deaths - has brought the most visible rift between a state government and Australia's federal government over the country's handling of the pandemic, which has included an emergency cabinet of leaders from both levels of government.

State Premier Daniel Andrews reintroduced tough movement restrictions in the state capital Melbourne in early August, including a nightly curfew, as most other states and territories relaxed lockdown measures.

The Victoria measures, due to end on the weekend, were broadly extended until Sept. 28, although with some small changes that eased some aspects of the restrictions.

Federal Health Minister Greg Hunt told radio station 3AW on Tuesday that Victoria might have avoided a second wave and been able to ease restrictions sooner if its virus tracing system was more than like that of New South Wales (NSW). Prime Minister Scott Morrison has warned of the cost of the Melbourne lockdown to the national economy.

Andrews, while not directly accepting criticism, said on Monday he would set up five "suburban" contact tracing teams specializing in geographic parts of the state, which would make it easier to target specific locations where people had been infected.

He said he would also send representatives to larger NSW, which has kept its daily new infection rate below 22 since April, to observe practices there "to double and triple-check that there's nothing that might be changed, or any insights, any experience".

Andrews said Tuesday's daily case figures showed Victoria was on the right track.

"I know those rules are not easy," Andrews said in a televised news conference.

"I think they'll be able to take some significant steps soon because the trend is with us, the trend is good," he added, referring to Victorians living in regional areas who are also under tough restrictions.

Neighboring NSW reported nine new cases in the 24 hours to Tuesday, while the northern state of Queensland reported one. Most other regions have been case-free for weeks.