Pro-Hamas graffiti prominently displayed on the day of a painful anniversary has been labelled "terrorist propaganda" as authorities consider if the anti-Semitic message constitutes an offence.

The words "Glory to Hamas" were painted 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.

The words "Free Palestine" and "Oct 7, do it again" were later found on the side of a building further along Alexandra Parade on the corner of Brunswick Street.

The graffiti appeared early on Tuesday morning, the second anniversary of the October 7 terror attacks on Israel by Hamas, which Australia has designated as a terrorist organisation.

Prime Minister Anthony Albanese said Australian Federal Police would wo

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