Premier Daniel Andrews says the government's hardline strategy will remain in place, despite the number of new cases staying relatively low.
A man in his 80s died in hospital, taking the state's toll to 15. Nine new cases have also been confirmed after 17 new cases reported on Saturday.
"These numbers do jump around a little bit, but the increases are small ... the strategy's working," Mr Andrews told Sky News Sunday Agenda.
The sheer number of people roaming around Victoria if the state's schools were opened during the coronavirus pandemic is why Mr Andrews is so adamant about keeping them closed.
He says having a million students roaming around the Victorian community, as well as 100,000 parents doing pick-ups and drop-offs at the school gates and tens of thousands of teachers attending school is not consistent with the national message to stay at home to protect the health system.
"Nor does it achieve anything other than spreading this virus," Mr Andrews told Sky News on Sunday.
"It's perfectly fine to send your kids to school if you can't have them learning from home, but if you can have the kids learning from home they must learn from home."
He expects the present school arrangements to remain in place for the whole of term two.
"If that were to change, if we're to continue to see very stable (COVID-19 case) numbers, if we continue to see this progress we are seeing, we would always reserve the right to look at those arrangements," he said.
Despite the improving situation, he said there would be no easing of social distancing restrictions and the plea for people to stay at home.
"We need to stay the course. It's frustrating, but it's certainly less frustrating than if you look at what happened in northwest Tasmania last week," he said, referring to a new cluster outbreak in the town of Burnie.
"This can get away from you very, very rapidly."
Seven of the new cases in Victoria are .
Since the state broadened the COVID-19 testing criteria, testing rates have risen, with thousands more being assessed in the last day or two.
The state of emergency in Victoria is due to expire on May 11 and authorities will set about removing social distancing restrictions in a "very thoughtful and careful way", Health Minister Jenny Mikakos said on Saturday.
Mass gatherings including sporting events and concerts may not happen until next year.
Anyone with symptoms of a new fever, chills or breathing problems - specifically a cough, sore throat or shortness of breath - can now be tested for COVID-19.
People in Australia must stay at least 1.5 metres away from others and gatherings are limited to two people unless you are with your family or household.
If you believe you may have contracted the virus, call your doctor (don’t visit) or contact the national Coronavirus Health Information Hotline on 1800 020 080. If you are struggling to breathe or experiencing a medical emergency, call 000.
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