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Australia reported its highest daily rise in COVID-19 cases on Monday, as it grapples with a surge in cases of the Delta variant.

The state of New South Wales recorded 112 new locally transmitted cases.

Most of the cases were in Sydney, marking three consecutive days of record case numbers.

State Premier Gladys Berejiklian said a majority of the cases were family members or close friends of already infected persons.

She urged people to follow the rules and stay at home: "Overwhelmingly we just want people to stay at home. The virus won't spread if people don't leave home. That's the bottom line. Don't leave home unless you absolutely have to."

Authorities warned that the lockdown for Sydney - which is entering its third week - could be extended.

Those measures include school closures and stay-at-home orders.

But there was a glimmer of hope for the city's five million residents as the number of newly infected people who were out in the community while infectious, dropped from the day before.

The Sydney outbreak has put Australia's sluggish vaccine rollout under scrutiny.

Just 11% of Australia's adult population of just over 20 and a half million have been fully vaccinated.