Victorian Chief Health Officer Brett Sutton said partial lockdowns to contain the spread of the virus were not off the table and foresaw the situation aggravating.
Victorian Health Minister Jenny Mikakos told reporters on Monday they were "obviously concerned" by the increase in the number of cases and the upward trend.
But authorities are yet to decide whether tighter measures on coronavirus hotspots should be imposed after Monday's new cases brought the state's confirmed total to 2099.
Ten cases have been linked to the Wollert family outbreak, four have been linked to a new family outbreak in Lysterfield and Pattersons Lakes, and five are a new family outbreak in Truganina.
"I expect there'll be at least as many positive cases as we've had over the last 24 hours".
Mikakos broke down the new cases as follows: one in hotel quarantine, 14 linked to outbreaks, 37 detected through routine testing, and 23 now being investigated to determine their origin.
Sutton said he would not announce the lockdown of any suburb on Monday, but it was still under consideration.
Sutton suggested suburb lockdowns could cause infected people to travel into non-infected areas if they became frustrated with restrictions.
Professor Sutton also said that forcing people to stay home if they have symptoms will be required.
He said: "The public health directions chasing the law is something we have to consider because we have to do whatever is required to turn this around".
"We have to think through what will make a difference in this current challenge ..."
"It is a hard situation and we are not on top of it yet", he said.
'Outbreaks are occurring across multiple households, across work and other settings'.
The schools are Queen of Peace Parish Primary School in Altona Meadows, Aitken Hill Primary School in Craigieburn, Fitzroy High School and Port Phillip Specialist School and St Bernard's College in Essendon.
Mikakos also said a number of schools would be deep-cleaned, following staff or students testing positive.
For the past 12 days, Victoria has recorded double-digit increases in coronavirus infections.
A childcare centre in Abbotsford also has a case.
The Lifeblood Redcross processing facility will also be cleaned after a staff member contracted the virus.