The force added: "During the July incidents, the male wore a Scream mask, which completely covered his face.”
Detective Inspector Martin McLean said that investigators believe the man is working alone.
"There's certainly a pattern of behaviour. It's always with a spray-can, and always targeting the synagogue," he said. “At this stage we have nothing to suggest he's working with anyone else.”
He went on: "We're certain that there are people out there who know this person or have seen this person either before or after.
"Police certainly take a dim view of this sort of abhorrent behaviour in the public arena.
"If we can have any help in regards to this matter that would be greatly appreciated.
“There is absolutely no place at all in our society for hate-based behavior."
Anyone with relevant information is asked to contact CrimeStoppers on 1800 333 000 or submit a confidential report online.
It comes just a month after another synagogue in Melbourne, the East Melbourne Hebrew Congregation, was set on fire with 20 people inside. All the worshipers managed to escape the building and there were no injuries.
Angelo Loras, a 34-year-old from New South Wales, had since been charged with reckless conduct endangering life, criminal damage by fire and possession of a controlled weapon. He denies the charges against him.
