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Chief Inspector Gary Coffey said the “disgusting” vandalism to the heritage-listed site would cost up to $20,000 to remove.
The two middle-aged men allegedly responsible can be seen on the footage moving casually around the site, appearing to spray a substance onto the walls, steps and floor.
Coffey said the men were at the memorial for 20 minutes and at one point even engaged with staff.
The men then left the memorial together and walked north through Hyde Park.
Cleaners are at the site today, attempting to remove the oil-based substance, which Coffey said had caused “permanent” staining to the granite.
“The war memorial is a sacred site to our community and to do this is absolutely disgusting,” Coffey said.
“Their actions to my mind were certainly deliberate.
“Someone will know them and they should be held accountable for their actions.”
The first man is described as Caucasian, about 50 to 60 years old, with a large build and black and grey hair.
He was wearing black sunglasses, a red and black check long sleeve shirt with a blue striped shirt underneath, light-coloured shorts, black boots with black socks and carrying a red shopping bag cart.
The second man is described as Caucasian, about 50 to 60 years old, with a solid build and shaved head.
He was seen wearing a dark blue button-up collared shirt, dark jeans and black sneakers with white trim and was carrying a brown and black man bag.
Anyone with information is urged to contact police.