"Within Victoria, 37 of the new cases are linked to outbreaks or complex cases and 360 are under investigation", said a statement from the Department of Health and Human Services in Victoria on Saturday.
Three weeks ago, the premier of Victoria state imposed what the country calls a "stage three lockdown" on Melbourne and surrounding areas.
Restrictions on movement and business operations elsewhere in the state will be less severe than in Melbourne.
Andrews said his government was deeply anxious that 49 "mystery cases" identified on Saturday could indicate the virus was spreading widely through the Melbourne community and confirmed he was in discussions with Australian Prime Minister Scott Morrison about tougher restrictions.
Premier Daniel Andrews announced on Saturday a man and woman in their 80s had died, along with a woman in her 90s.
Dr Chris Moy, from the Australian Medical Association, said Victoria must act "now or never" and implement a New Zealand style lockdown to control the deadly second wave.
Andrews said further restrictions were needed to act as a "circuit breaker" to curb community transmission, as he acknowledged tougher restriction would take an economic toll. "This is the only option we have".
"Numbers are too high and there is a growing case for us to do more", he said.
"Even minor changes have a significant cost. What we may be doing now may not be enough". Andrews on Saturday announced another 397 new coronavirus infections, and expressed deep concern about the number of mystery cases it couldn't trace to a known outbreak.
"We can't open up again at these sorts of levels and therefore there's very detailed work being done about what possible next steps might look like", he said.
Andrews said hospital nurses had now worked more than 570 shifts in care homes.
"There's no question these are very hard times in Victoria".
Mr Andrews' announcement comes as a map of the state revealed a grim insight into the severity of coronavirus infections in Victoria. This brings the state's deaths in the pandemic to 116 and Australia's tally to 201.