Federal Greens deputy leader Adam Bandt, who arrived on Saturday morning outside one of the polling booths, blasted Labor for its record, calling it "unfit" to serve as the state's opposition party.
"It has run a negative campaign based on limping over the line
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with a preference deal from Family First," he told reporters.
"It's a reflection of whether Labor considers itself a progressive party, capable of working with other progressive parties like the Greens, or whether they are wanting to go in different direction."
Local Greens candidate Cathy Oke said she hopes her efforts in running a positive campaign focused on local issues will pay off.
"We'll be creating history here in Melbourne if we have a lower house representative," she said of the battle to pull the seat away from Labor, which has held Melbourne for more than a century.
"But I don't underestimate how close it's going to be."
Labor's Jennifer Kanis is the other frontrunner in a field of 16 candidates.
Polls close at 6pm (AEST) on Saturday, but a final result could take some time with complicated preference deals likely deciding the winner.
The Liberal Party is not running a candidate.
A spokeswoman for the Victorian Electoral Commission said on Saturday that all polls had opened on time at 8am with no reports of any problems so far.
