Australia's second-biggest city of Melbourne reported a record rise of more than 400 new coronavirus cases on Friday despite a week-old lockdown of more than 5 million residents.

Authorities in the state of Victoria, which surrounds Melbourne, said there were 423 new infections in the metropolitan area and five more in rural parts of the state.

The total was higher than any single daily increase in COVID-19 cases for the entire country since late March.

"We have not turned the corner here, worse than that," said Victoria's chief health officer, Brett Sutton.

Melbourne has been experiencing a surge in coronavirus infections since mid-June, after the rest of the country had successfully contained the epidemic.

The Melbourne outbreak was initially blamed on health and security breaches at hotels where returning international travellers were under quarantine.

Residents in and around greater Melbourne were ordered into a six-week stay-at-home lockdown a week ago in a bid to contain the virus, and officials said they would give those restrictions more time to counter the outbreak before considering tougher measures.

Melbourne
Melbourne has been experiencing a surge in coronavirus infections since mid-June, after the rest of the country had successfully contained the epidemic Photo: AFP / William WEST

"There is a hope that the numbers stabilise over the coming days," Sutton said.

But he added: "No one is being complacent here, and we are all thinking about the additional measures that may be required if it does not turn around."

Australia's other states and territories have all closed their borders to people from Victoria in a bid to stop that outbreak from spreading.

But the contagion has already reached Sydney, where there have been growing numbers of locally transmitted COVID-19 cases in recent days after an initial cluster erupted due to an infected Melbournian visiting a popular pub.

There have been 42 virus cases linked to that pub, but officials on Friday reported several other infections with no clear link to that cluster.

The spread prompted authorities to again tighten restrictions on the number of people allowed into restaurants or to attend public gatherings like weddings and funerals in the greater Sydney area.

Nationwide, Australia has reported just over 11,000 cases of COVID-19 out of a population of some 25 million, with 116 deaths.

The vast majority of cases have been in Victoria and New South Wales, which surrounds Sydney, with other regions reporting no new cases of locally transmitted infections for weeks.

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Australia COVID-19