The Premier defended the health department's efforts from growing criticism on Monday, but acknowledged that more resources were needed to respond to the "massive task" of working through the growing backlog of active cases requiring tracing or investigation.
"It is a big, big task.
They are doing their very best. That is all you can ask of people," he said. "The team is getting bigger and it needs to because the task has never been bigger."
Up to 1400 Australian Defence personnel have joined Victoria's virus response team, including many working and overseeing the contact tracing teams who have also been joined by private call centre staff from Telstra, Medibank, Qantas and banks NAB and CBA.
Mr Andrews urged those who tested positive and their close contacts to show "common sense" and stay at home until authorities contacted them.
"My advice, my message to those who test positive – if you get confirmation that you have tested positive, then you shouldn't need someone to call you to know that you have to stay home.
"And your close contacts, they need to stay at home as well. People in your family. You will be contacted as soon as is possible."
Colac in south-west Victoria is running its own contact tracing program, after what local Liberal MP Richard Riordan described as a "woefully slow" response from the Department of Health and Human Services (DHHS) to an outbreak at the Australian Lamb abattoir in the town.
There have been 12 cases linked to the abattoir since a contractor working at the facility tested positive on Friday, including one at Trinity College Colac.
"We would still not know what we have in this town if it were up to DHHS," Mr Riordan said.
"There's clearly a lack of resources and a lack of communication. We've had no information as to when or where the first person caught it, or how it come to town.
"The only reason there's information now is because the community, abattoir and hospital got together and did their own contact tracing. We're 72 hours into known cases and nothing has been done by DHHS."
He said the level of contact tracing the government needed to do was "going to be a nightmare" and was "getting worse by the day" as new cases continued to grow.
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