Premier Daniel Andrews said two of Victoria's three new coronavirus cases are under investigation, with another linked to a known outbreak.
Mr Andrews' remarks come as Victoria recorded three new COVID-19 cases since Wednesday.
There are five Victorians in hospital receiving treatment for coronavirus, as more than 24,000 tests were conducted on Wednesday.
There are no active cases in regional Victoria, Mr Andrews said.
As Melburnians were released from lockdown on Wednesday, Mr Andrews fielded questions about reopening state borders, particularly with NSW.
"They (NSW) have made it abundantly clear they want to see how things unfold," Mr Andrews said.
"I know it's frustrating, but I can't give people a date."
The state border with NSW closed in early July, with residents of border communities acquiring permits to allow travel across state lines.
ANOTHER three new COVID-19 cases have been recorded in Victoria.
The Department of Health and Human Services on Thursday said there were no further coronavirus deaths recorded.
The rolling 14-day case average for regional Victoria remained at zero.
Thursday's data brought the rolling average for metropolitan Melbourne down to 2.4, with the state average also sitting at 2.4.
The number of mystery cases in Melbourne also increased to four.
It came after the state recorded two new cases and two deaths on Wednesday.
The two deaths were aged care residents who died from the virus some weeks ago but were added to the state's toll on Wednesday.
The state had recorded no new coronavirus cases or deaths on Monday and Tuesday.
It was the first time since early March that there had been consecutive days of zero COVID-19 cases.
Premier Daniel Andrews on Wednesday confirmed there were no active coronavirus cases in regional Victoria.
The final two cases in Greater Shepparton were cleared after the residents tested negative to the virus.
One of Greater Bendigo's total COVID-19 cases was also reclassified on Wednesday, bringing the total case numbers down to 99.
There were only 80 active coronavirus cases across the state on Wednesday.
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