The state recorded 24 new locally acquired coronavirus cases on Tuesday, with 10 potentially infectious while in the community.

There are now more than 510 exposure sites, with over 50 sites stretching from South Melbourne to Brighton.

The health department is asking anyone who lives or spends time in Glen Eira and Port Phillip local government areas to get tested if they have been to exposure sites, have any symptoms or “even if they are unsure”.

Five mystery cases in the beachside suburb of St Kilda are worrying Chief Health Officer Brett Sutton.

“We want to see more tests right across the area because it’s becoming a real concern for us,” Professor Sutton said in a Tuesday night COVID update.

“We need more tests to track down unidentified chains of transmission and protect the whole local community.”

Melbourne is 13 days into its sixth lockdown, which was extended on Monday until September 2.

A 9pm to 5am curfew, which was in place during the state’s second wave, has been reintroduced, with playgrounds and other outdoor facilities closed and exercise limited to two people.

-with AAP