Prominent pro-Hamas graffiti that appeared above a major road on a painful anniversary has been labelled "terrorist propaganda", as police investigate the anti-Semitic message.

"Glory to Hamas" was painted on a large billboard above a shop on the corner of Alexandra Parade and Brunswick St in Fitzroy in Melbourne's inner north.

The words "Free Palestine" and "Oct 7, do it again" also appeared on the side of a building further along Alexandra Parade on the corner of Smith St.

The graffiti was found 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 work with Victoria Police to bring the perpetrators to justice.

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