Australia's two largest cities are set to stay under tight COVID-19 restrictions as Melbourne on Monday extended a five-day snap lockdown designed to curb a virulent outbreak.

"These restrictions simply cannot end at midnight tomorrow night," Victoria state premier Daniel Andrews said, without saying how long the Melbourne lockdown would last.

About 12 million people are under lockdown in Melbourne and Sydney, where a month of restrictions has failed to quash an outbreak of the Delta variant.

Australia had mostly dodged widespread community transmission in the 18 months since the pandemic began, but is now seeing more than 100 new cases a day, straining contact tracing efforts.

The most recent outbreak started mid-June when a foreign aircrew infected a local driver in Sydney.

The virus was then carried to Melbourne with a relocation team, prompting a snap lockdown that was due to end late Tuesday, but has failed to reduce new infections to zero.

Victoria state on Monday reported 13 new cases.

Andrews told weary residents now on their fifth lockdown that the measures were making an impact. "We have made great progress, we have avoided thousands of cases," he said.

In Sydney, it looks increasingly unlikely that the city will exit a lockdown in its fourth week at the end of the month as planned.

On Saturday New South Wales introduced a slew of new restrictions and ordered all non-critical stores to close.

The state reported 98 new cases on Monday.