In the inner city, dozens congregated for a takeaway-drink pub crawl event on the streets of Richmond on Saturday, while in Northcote about 200 people gathered for a street party.

On the Mornington Peninsula, one resident had made plans to invite a thousand people to a house party with a DJ and a stage.

There are also reports of a 100-person engagement party held in Melbourne which a COVID-positive guest may have attended.

An online account for Melbourne's Jewish community has advised a community member has tested positive and visited supermarkets in Balaclava while infections.

It is believed they may have attended the engagement party.

Acting Superintendent Greg Hinton told reporters on Sunday police had increased patrols and were examining social media activity, and also looking into liquor licensing breaches.

News of the illegal gatherings comes as the state records 25 new local infections and the end of lockdown recedes from view.

Premier Daniel Andrews told reporters that illegal visits and gatherings are "not worth it".

"None of us should be doing anything that potentially spreads this virus," he said on Sunday.

Health authorities say 21 of the cases are linked to known outbreaks and 12 have been in isolation throughout their infectious period.

The unlinked cases include a cleaner in Greater Dandenong, a construction worker in West Footscray and two St Kilda cases.

More than 65,000 vaccine doses were administered in Victoria on Friday as the state aims for one million jabs over five weeks.

With AstraZeneca abundant and from Monday available at all state-run vaccination centres to those over 18, Mr Andrews said Victorians should get the jab immediately.

He said they should neither wait for Pfizer nor change their plans given the imminent arrival of one million Pfizer vaccines from Poland. Victoria will get 175,500 of those extra vaccines.

The Victorian government would also open up an additional 84,000 vaccination appointments on Sunday and Monday

"No one should delay on the basis that more is coming. Yes, there's more coming, but when that occurs, who knows?" Mr Andrews said.

Almost 47 per cent of eligible Victorians had received one vaccine dose as of Friday, while more than 25 per cent were fully vaccinated.

Mr Andrews declined to discuss the potential extension of lockdown settings in Melbourne, scheduled to conclude on Thursday, but admitted the number of mystery cases remains too high.

If the mystery case number does not dip, lockdown may be extended.

"If we were to reopen the whole economy, if we were to reopen and let people move freely right now, then we would finish up where Sydney's at - thousands of cases," Mr Andrews said.

As of Sunday, there were more than 500 exposure sites spread across multiple Melbourne suburbs, including the Royal Melbourne Women's Hospital and Chadstone Shopping Centre.

Some 13,000 people in Victoria are in 14-day isolation stints.

For exposure sites visit www.coronavirus.vic.gov.au/exposure-sites

Australian Associated Press