Police are investigating anti-Semitic graffiti daubed on a prominent billboard at a major capital city intersection on the anniversary of the October 7 terror attacks on Israel.

The words "Glory to Hamas" appeared in black lettering on a large billboard above a shop on the corner of Alexandra Parade and Brunswick Street in Fitzroy in Melbourne's inner north on Tuesday.

Victoria Police confirmed the force was investigating criminal damage to the sign and said it was found at about 7.15am.

Anyone with information about what happened has been urged to come forward.

"There is absolutely no place at all in our society for anti-Semitic or hate-based symbols and behaviour," a spokesperson said.

The words "Free Palestine" and "Oct 7, do it again" were later found on the side of a building fur

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