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Premier Daniel Andrews confirmed on Sunday a man in his 70s has died from the virus overnight, taking the national toll to 108.
"We send our best wishes and assure that family that our thoughts and prayers are with them. This will be a very, very difficult time for them," he said.
It comes after a man in his 90s died from the virus on Friday.
The state now has 3799 Covid-19 cases, of which 1484 are active.
There 57 people currently in hospital with the virus and 16 of those are in intensive care.
Victoria's Chief Health Officer Brett Sutton said outbreaks in health and aged care settings were of particular concern.
There are 11 coronavirus cases linked to Brunswick Private Hospital, eight to the Alfred Hospital and two to Box Hill Hospital.
Eleven people have also tested positive at a single aged-care facility.
"The workforces know what to do, but it is a risk that can't be mitigated down to zero, and my thoughts go to those front-line workers," Professor Sutton said.
"I have been an emergency department doctor for years and they are brave and they are brilliant in responding to the challenges of positive cases that need to be managed there."
There are also 22 cases linked to public housing in Carlton.
"They are in towers. They are not as high-risk as the towers in North Melbourne, in Flemington, but all towers - where there is a concentration of people - are at-risk settings," Professor Sutton said.
The premier said he was grateful to the almost 32,000 people who were tested for the virus on Saturday.
"Arguably there is nothing more important than coming forward if you've got even mild symptoms," Mr Andrews said.
The state has recorded a week of triple-digit increases in new cases, including a record 288 infections on Friday.
Melbourne and the Mitchell Shire are again under stage three restriction until August 19 because of the spike in new cases.
People in those areas are only allowed to leave home for four reasons: to shop for food and supplies; to receive or provide care; to exercise; and study or work if they can't do so from home.
"These next six weeks are not an ordinary winter. We all have to play our part, we cannot ignore the circumstances we face," Mr Andrews said.
"Nobody wanted to be in this position, but this is where we find ourselves."