SYDNEY: Australian authorities on Tuesday vowed to crank up policing of anti-COVID lockdown rules in Sydney, but dismissed suggestions that tougher measures, including a curfew, were needed after the city reported its biggest single-day new case number yet.

With more than five million residents of Australia's biggest city now in lockdown for more than six weeks, Sydney reported 343 new infections in an outbreak stoked by the spread of the highly transmissible Delta strain of COVID-19, up 66 from the day before and topping the last one-day peak set on Saturday.

Authorities in New South Wales (NSW) state, home to Sydney, also announced three deaths from the virus, all of them unvaccinated. A total of 357 cases are in hospitals, with 60 in intensive care, 28 of whom require ventilation.

With just under 36,700 cases and 942 deaths, Australia has handled the pandemic much better than many other developed economies. But the Delta strain has thrown Australia's reopening plans in disarray, as authorities seek to ramp up a vaccination rollout that critics of Prime Minister Scott Morrison have slammed as being too slow and ineffective.

Amid questions about the effectiveness of Sydney's lockdown, under which residents are supposed to stay at home bar essential movements, NSW authorities said police have been asked to step up checks on how many people were being allowed inside small shops at the same time as they were still seeing "lots of unnecessary movement of people".

"What I'm concerned about is the crowding in shopping centres and places where we have seen transmission events in small shops," state Chief Health Officer Kerry Chant told reporters.

State officials have set a target of six million vaccinations by the end of the month - when the Sydney lockdown is currently scheduled to end - if curbs are to be eased. So far more than 4.5 million total shots have been administered in New South Wales, with more than 23% of people above 16 fully vaccinated.

"This is why we've had a sense of urgency about the jab ... because that gives us a chance to see what people can do in September and October," state Premier Gladys Berejiklian told reporters in Sydney.

Meanwhile NSW officials expanded strict stay-home rules to include two regions near the Queensland border, Byron Bay and Tamworth, late on Monday after visits by infectious people from the city.

Australia's Victoria state reported a slight rise in new COVID-19 cases on Tuesday, raising the prospect of an extended lockdown in Melbourne, the country's second-biggest city, beyond Thursday.

Authorities reported 20 new cases, up from 11 a day earlier. In line with recent trends. Worrying officials, 15 of the cases were in the community while infectious.

Economists expect the lockdowns in Sydney and Melbourne to have tipped the country's A$2 trillion ($1.5 trillion) economy into a second recession in as many years, with a contraction expected for the quarter through September.

"There are big challenges for the economy, but I want people ... to be confident, to be optimistic and to know there is going to be light at the end of the tunnel," Federal Treasurer Josh Frydenberg told broadcaster Seven News on Tuesday.