The government leader imposed a warning that the city of Melbourne would continue its lockdown as Covid-19 infected people continue heading to work.
Melbourne is half-way through a six-week lockdown that has been enforced to stop the community spread of the Covid-19 virus.
Compulsory mask-wearing rules in Australia’s second-largest city have been in place since last week.
The new Covid-19 cases followed by the six deaths reported on Monday surpass a previous record of 484 new Covid-19 cases reported last Wednesday.
Victoria Premier Daniel Andrews said the biggest source of the new infections is people continuing to go to work after showing symptoms.
“This is what is driving these numbers up and the lockdown will not end until people stop going to work with symptoms and instead go and get tested,” Andrews said.
Prime Minister Scott Morrison called for patience in Victoria.
“There has been significant community transmission in Victoria. That will take some time to get on top of,” Morrison said.
Australian Deputy Chief Medical Officer Michael Kidd said New South Wales is the only other state or territory to record new Covid-19 cases in the last 24 hours.