Australia has recorded its lowest one-day rise in coronavirus infections in more than three weeks, as Melbourne remains under strict lockdown.

Official data on Thursday showed there were 292 new infections in the past 24 hours, down from 428 on Wednesday.

It is the lowest daily total since 20 July. Victoria had by far the most infections - 278. Its capital Melbourne began its shutdown on 3 August.

Health Minister Greg Hunt voiced cautious optimism about the new data.

"We now believe, cautiously, that we have early signs of the flattening of the curve," he said.

In Melbourne, workers must carry a permit to leave home, and all non-essential businesses have been shut. Mask-wearing in public is also compulsory.

For more than a month the city's residents - nearly five million people - have been required to stay at home except for essential shopping trips, medical care or exercise.

The authorities have warned that Melbourne's Stage Four lockdown could be extended to other parts of Victoria if outbreaks in Geelong, Ballarat and Bendigo - towns just west of the city - are not brought under control.

"It's not time to be complacent, it's 'yes, this worked, we're on the downhill slope, pedal harder'," said Prof Catherine Bennett, an epidemiologist at Deakin University.

According to the global tally kept by Johns Hopkins University, the number of Covid-19 deaths in Australia has reached 361 and the total number of officially confirmed cases is 22,358.