The Australian state of Victoria has finally brought its second wave of Covid-19 cases to an end, becoming one of the world's more successful governments at doing so.

The state of about 6.7 million residents recorded just three new cases yesterday. On Tuesday, it recorded only one case, a person who tested positive in July and is believed to be a rare case of reinfection.

This is a dramatic turnaround from early August, when new daily coronavirus cases peaked at 687.

That was due to an outbreak that is believed to have originated from security guards who became infected while working at quarantine hotels.

But Victoria's measures to curb the outbreak proved controversial.

The state government placed its capital city Melbourne under strict lockdown, closing schools and many businesses. It also imposed a nightly curfew, which ended last month.

Stringent measures remain in place, even though new cases of infection have averaged three per day over the last week.

The government eased restrictions from the start of this week, but dining at cafes and restaurants and working in offices are still prohibited. Most retail stores are closed, Melbourne residents cannot leave the city, and gatherings are limited to 10 people. These restrictions are due to be further eased from Nov 2, as long as case numbers remain low.

Victoria's Premier, Mr Daniel Andrews, has come under heavy pressure over his cautious approach.

"We have to deal with the health problem first," he said yesterday.

Commenting on the apparent reinfection, he said: "It is through an abundance of caution that we are assuming that is a positive case, rather than the person shedding after the original infection."

The state's second wave appears to have taken a personal toll on the Premier, particularly as he and his government have been heavily blamed for hotel quarantine breaches and inadequate contact tracing.

As a result, Mr Andrews has seemed determined to completely crush the virus and avoid any risk of its return.

But he is facing intense and growing criticism over his refusal to swiftly reopen the economy.

The Federal Treasurer, Mr Josh Frydenberg, launched a savage attack on Mr Andrews this week, accusing him of "unforgivable" stubbornness.

Mr Frydenberg, who lives in Melbourne, said Victoria is home to 26 per cent of Australia's population, but accounted for 40 per cent of the nation's unemployed workers.

"There's been a callous indifference by the Victorian government to the loss of jobs in the state and the plight of small business," Mr Frydenberg said in a video he posted online.

"More than 1,000 Victorians have lost their jobs every day as a result of the lockdown... The bloody-mindedness is unforgivable."

Business groups have also attacked Mr Andrews, saying the easing of restrictions has been too slow.

In a joint letter to Mr Andrews, the heads of seven major Australian firms, including BHP and the Commonwealth Bank, urged him to expedite the opening of the economy.

"We urge you now, in light of the excellent recent progress, to permit the careful and staged return to the workplace of office workers and the small businesses that provide services to them," said the letter, according to Tuesday's report in The Sydney Morning Herald.

But Mr Andrews appears to have the public on his side.

An opinion poll in The Australian late last month found 62 per cent of Victorians believed the Premier had handled the crisis well, 34 per cent thought he had handled it badly and the remainder were uncommitted.

Mr Andrews continues to defiantly stand by his approach. On Monday, he attacked Mr Frydenberg for "(playing) politics in the midst of a global pandemic".

"Victorians want their family protected, they want their health issues dealt with so we can open up," he said.