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The health department on Monday confirmed 202 cases were linked to known outbreaks, with the source of the remaining 271 infections under investigation.
It is the highest daily tally of the state's latest outbreak and brings the total number of active cases to 3507.
In the 24 hours to Monday morning, 49,037 tests were processed and 30,032 Victorians received a vaccine dose at a state-run hub.
It comes as authorities investigate a Covid-19 outbreak at the Fitzroy Community School in Fitzroy North, which has repeatedly flouted lockdown restrictions by inviting parents to send their children to class.
Deputy Chief Health Officer Dan O'Brien on Sunday said at least 30 students and staff had contracted the virus.
There are about 60 students enrolled at the school, which describes itself as an "independent, alternative primary school".
Currently, only children of permitted workers and those who are vulnerable are allowed to attend school in Melbourne.
School founder Faye Berryman told ABC News 24 primary-aged children have "a strong resilience to Covid".
"Children's emotional wellbeing, their feeling of insecurity, the unpredictable long-term psychological danger of raising them under a mantle of fear are the price we pay for not having children at school," she said.
More than 3800 children under 12 have contracted coronavirus across Australia between January 1 and September 2.
Of those, 134 have been hospitalised while three have been admitted to intensive care.
Meanwhile, the state government is continuing its development of a roadmap out of lockdown.
While the regions emerged from lockdown late last week, coronavirus restrictions will not ease for Melburnians until 70 percent of eligible Victorians have had their first dose of a Covid-19 vaccine.
When that target is reached, Melburnians will get an extra hour of outdoor activity and the five-kilometre travel radius will be expanded to 10km.
By Sunday, 66.2 percent of the eligible Victorian population had received at least their first dose.
There has been no indication of what freedoms will be permitted when more than 70 per cent of the population is double-vaccinated.
But Premier Daniel Andrews has flagged the state government will release a comprehensive roadmap out of lockdown "in about a week's time", based on modelling from the Burnet Institute.
Returning students to classrooms, including upgrading ventilation in schools and staggered entry times, will form part of the plan.
Schools and Covid-hit areas are preparing to welcome a series of pop-up vaccination hubs to boost coverage rates, with the programme to begin over the next two weeks.
From Monday, children aged 12 to 15 became eligible for the Pfizer vaccine in the state.
Of the 392 new cases reported on Sunday, 255 were from Melbourne's north and another 89 from the western suburbs.
The federal government has embarked on a three-week vaccination blitz of the areas, allocating an extra 417,000 Pfizer and Moderna doses to Victoria.
Meanwhile, most regional Victorian train services remain suspended on Monday as 300 V/Line employees isolate after five positive tests among drivers and operational staff. Coaches are replacing most services.