Eleven infections have been detected in the 24 hours to midnight on June 6, although two were already reported by aged care operator Arcare.
The Arcare Maidstone outbreak has grown to six cases after another resident and a registered nurse tested positive.
The 79-year-old resident, who had both doses of the Pfizer vaccine, was moved to hospital as a precaution.
A first dose had been given to the registered nurse, who last worked at the nursing home on June 5.
“The staff member had not worked at other facilities,” the Department of Health said.
There were 24,265 test results received and 17,719 vaccine doses administered on June 6 as Melbourne spent its second weekend in lockdown.
It is unclear whether the latest glut of cases will dent the city’s hopes of moving to eased restrictions from June 4.
Victoria’s Deputy Chief Health Officer Allen Cheng said officials’ main concern is tracking down “upstream” transmission.
“Given five percent of Victorians have been tested in the last seven days, if there was a big outbreak going on I would expect to have picked it up,” he told reporters on June 6.
“That risk does fall over time but we are still concerned about that and that is where all our efforts are going.”
Professor Cheng said there was no “magic number” of people getting the jab to avoid future lockdowns, with only two to three per cent of Victorians fully vaccinated.
“Once you get up to much higher coverage rates, then it makes a whole lot of things easier,” he said.
“We may not need the intensity of restrictions. We may be able to only do contact tracing without having to do other things quite to the same level, and that is the benefit of vaccination.”
Federal Health Minister Greg Hunt on June 6 announced an additional 100,000 vaccines are being made available for Victoria.
The federal government has also extended its suspension of JobSeeker mutual obligation requirements until June 15.
Ten people are now infected with the Delta variant as part of the West Melbourne outbreak, with investigators still unsure how it spread into the community.
Authorities are continuing to comb through genomic sequencing data from across the country for answers.
“We have theories. We’re working through those,” Cheng said.
More than 1900 primary close contacts of the original Kappa variant-related Whittlesea outbreak were released from isolation on June 6.
Six train services from Merlynston Station to Flinders Street Station were added to the list of over 350 exposure sites late on June 6 evening.
By Callum Godde in Melbourne