The virus has spread rapidly among vulnerable residents in aged-care centers, where government disaster relief teams have been deployed to replace infected staff.
Outside Melbourne, the rest of Victoria will move to a Stage 3 lockdown from midnight Wednesday with people allowed to leave home only for essential work, study, care, and needed supplies.
Elsewhere in Australia, other states and territories have for weeks reported few or no new cases while relaxing restrictions.
They have, however, banned visitors from Victoria and Sydney — another virus hotspot.
New South Wales Premier Gladys Berejiklian said people were now being "strongly encouraged" to wear masks, particularly on public transport, in shops and at places of worship as the state attempts to avoid the fate of neighboring Victoria.
"We are holding the line and doing OK but I cannot stress enough that the next few weeks will make or break us, in terms of the way we get through this pandemic," she told reporters in Sydney.
Berejiklian added that unlike in Victoria, masks were not compulsory but would instead act as a "fourth line of defense" after testing, social distancing and hand-washing.
Australia's total reported infections reached almost 18,000 on Sunday, with 208 deaths in a population of 25 million.
(Writers: HR/FOX, Agence France-Presse)
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