Captain Cook statue vandalised in Sydney's eastern suburbs

New South Wales police are investigating after a Captain Cook statue was vandalised in Sydney's eastern suburbs.

The statue on the corner of Belmore Road and Avoca Streets in Randwick was vandalised earlier this month.

"We are currently working with local police who are investigating the matter and we have also engaged heritage stonework specialists to repair the monument," Randwick City Council said on social media.

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"As a council we condemn all acts of vandalism."

A photo of the vandalised statue drew mixed reactions on social media.

Police visited the site on Monday to assess the damage as a part of the investigation.

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"As inquiries continue, anyone with information about this incident is urged to contact Crime Stoppers on 1800 333 000," NSW Police said in a statement.

The investigation comes after another Captain Cook statue in Melbourne's Fitzroy Gardens was sawn off at the ankles.

Officers believe a group of four unknown offenders attended the gardens in Wellington Parade between 5pm on Sunday and 7am on Monday.

The statue was vandalised and toppled to the ground before footage of the incident was published online with the message: "The colony will fall."

Melbourne University political science Professor Sarah Maddison told 9News the vandals had a "valid argument".

"It's one way of saying we've got work to do. We have conversations that still need to be had," Maddison said.

"Where political leadership is absent, I think activism is inevitable."

Two colonial monuments were also targeted in Melbourne ahead of Australia Day.