MELBOURNE (REUTERS, BLOOMBERG) - Restrictions on gatherings will be imposed in Australia's second-most populous city of Melbourne as the authorities race to clamp down on a small Covid-19 cluster and find the missing link in a fresh outbreak that has grown to five cases.

Private gatherings in homes will be limited to five visitors a day from 6pm Melbourne time (4pm Singapore time) on Tuesday (May 25), while public gatherings will be restricted to 30 people, Acting Premier James Merlino told reporters in Melbourne.

"This is a responsible step that we need to take to get on top of this outbreak," he said.

Masks will be mandatory when indoors in public spaces for people aged 12 and older, including in workplaces.

The authorities said on Tuesday that they had identified one more case of community transmission since Monday, when four cases were found in the city's northern suburbs.

Genome sequencing has confirmed the cases are linked to a leak from a hotel used for quarantine in South Australia state earlier this month, Mr Merlino said.

The latest outbreak ends Victoria state's run of zero cases for nearly three months. The state, Australia's second-most populous, controlled the outbreak only after one of the world's longest and strictest lockdowns.

Australia has been successful in controlling the virus through rigorous testing and contact tracing and by closing its international border to non-residents - apart from a new travel bubble with New Zealand. But cases have sometimes leaked into the community from hotels where returned overseas travellers have to quarantine for 14 days.

One new locally acquired case has been reported in Melbourne, Mr Merlino said on Tuesday, a day after four infections were reported in the city.

All five cases belong to one extended family across different households and could be traced back to the variant found in an overseas traveller who returned to Melbourne early this month after completing quarantine in the city of Adelaide.

The authorities, however, said they could not yet find how the latest cases contracted the virus from the overseas traveller.

Thousands have been ordered to self-isolate and undergo Covid-19 tests, with health alerts issued for several sites, including one of the largest shopping centres in the country.

One of the cases had a high viral load while he visited some venues, prompting the authorities to warn Melbourne's five million residents to brace themselves for more positive cases in the next few days.

Vaccine hesitancy

The fresh outbreak comes as the authorities try to ramp up a sluggish national vaccination drive, with health experts worried that many Australians were delaying getting inoculated because of the country's success in effectively eliminating the virus.

Mr Merlino stressed the importance of getting vaccinated urgently in the wake of the new cases and said the government has plans to expand the vaccination eligibility criteria to roll out doses to more people.

"There are right now millions of Victorians who are eligible to be vaccinated. They shouldn't wait for tomorrow, they shouldn't wait for next week. They should move now and get vaccinated," he said.

Speedy tracing systems, movement curbs and social distancing have largely helped Australia to contain Covid-19 outbreaks. The country has recorded just over 30,000 cases and 910 deaths since the pandemic began.

Prime Minister Scott Morrison's government is under pressure to speed up the pace of the vaccine roll-out. About 3.6 million people in the nation of 26 million have received their first jab.