Australia's second-largest city Melbourne extends its lockdown in a bid to stamp out an outbreak of coronavirus on Wednesday.

Five million people in Australia's second-largest city will remain under stay-at-home orders for at least another week as Melbourne extended its lockdown on Wednesday in a bid to stamp out an outbreak of COVID-19.

Meanwhile, authorities in Sydney said they were considering easing restrictions for vaccinated residents despite the delta variant continuing to spread.

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The city entered its sixth pandemic lockdown last Thursday after a fresh Delta variant cluster emerged at a Melbourne school and quickly spread.

A street scene in Melbourne: the fresh Delta variant cluster emerges quickly in the city.

Daniel Andrews, the premier of the state of Victoria, said lockdown rules will be extended until at least August 19, after 20 new cases were detected overnight including several "mystery" cases.

"There are too many cases, the origins of which are not clear to us... for us to safely come out of lockdown now," he said.

"If we were to open, then we would see cases akin to what is happening, tragically, in Sydney right now," Andrews told reporters in Melbourne, referring to an outbreak in Australia's most populous city that has spread to thousands despite Sydney being in week seven of its own lockdown.

Sydney entered its sixth pandemic lockdown last Thursday.

"We have seen a surge in the number of cases and (that is) expected to continue," New South Wales state Premier Gladys Berejiklian told reporters in Sydney, reporting another 344 new infections in the past 24 hours, close to the city's single-day record.

Berejiklian said the Sydney lockdown, which has grown to include several areas north of the city, will also be expanded to include Dubbo, a small city about 400 kilometres (248 miles) northwest of Sydney.

Desperate to restart some major employment industries, New South Wales has allowed some in the most-affected Sydney suburbs to return to construction jobs around the city, but they must first be vaccinated.

New South Wales has allowed people to return to their jobs but they must first be vaccinated.

"I didn't want to get the vaccine ... but I needed to get the jab or I don't have a job," said Nick, a 31-year-old man who drives for an engineering company. He declined to give his surname.

Australia has so far fared much better than many other countries in the developed world during the pandemic, with just under 37,000 COVID-19 cases. The death toll rose to 944 on Wednesday after two people, including a man in his 30s, died in Sydney.