Victoria recorded five new locally acquired coronavirus cases on Saturday.
There was also one reported infection in hotel quarantine.
The state now has a total of 78 active cases, and the outbreak stands at 69 infections.
According to the Health Department, there were also 24,263 vaccine doses administered and 36,362 test results received in the past 24 hours.
The new figures come after it was revealed that the "Delta" strain of coronavirus had been found in seven people in Melbourne, including three children.
B. 1.617.2 is the same coronavirus strain that has decimated India.
US-based epidemiologist Eric Feighl-Ding explained the Delta variant was 50-70 per cent more transmissible and patients were 2.7x more likely to be hospitalised than other variants.
He said about 75 per cent of all cases in the UK were the Delta variant.
An urgent search is now underway to find the source in Melbourne after genetic testing showed the strain had infected at least two people in a family of four who travelled to NSW's Jervis Bay in late May.
Worryingly, the strain has not been traced back genetically to any existing Delta infections, including those in hotel quarantine.
Acting Victorian Premier James Merlino announced on Wednesday the initial "circuit breaker" lockdown would be extended by another week for Greater Melbourne.
Under the restrictions, people can only leave their homes for one of five reasons: to shop for food and supplies, authorised work and education, care and caregiving, exercise for a maximum of two hours a day and with one other person, and to getting vaccinated.
Merlino has said the state's lockdown timetable will stay in place despite two previous cases being reclassified as false positives.
"The proposition put forward by public health was that we needed this further seven-day period for Greater Melbourne to absolutely run this thing to the ground, and that remains the case," he said.
"We've got a high number of cases, many of them have some concern to public health. There are a number of other cases where we've seen fleeting contact and transmission."
Merlino said Victoria could not "risk [the virus] running away from us".