THE "knuckleheads" who vandalised the Cenotaph in Sydney's Martin Place may have been drunken overseas visitors who didn't understand the war memorial's significance, police say.

CCTV footage shows two men climbing on the east-facing statue of a soldier in Martin Place about 3am (AEDT) on Saturday.

One man climbed on top of the statue, put a witch's hat on its head and had his photo taken.

Shortly afterwards a second man removed the witch's hat, put it over the soldier's bayonet and swung from it, bending it.

Two men were then seen interfering with plants in a nearby flower bed.

Rocks Local Area Command Crime Manager Detective Inspector Damian Loone described the men as "disrespectful knuckleheads" and said police were determined to bring them to justice.

On Wednesday he appealed for anyone with information to come forward.

"We're coming up in a few months' time to the services of Anzac Day and also other services," he told reporters.

"It's important that these people come to the police and speak with us about this matter."

Their "idiotic" behaviour was probably explained by alcohol, he said.

"(It's) three o'clock in the morning - they wouldn't be out having a cup of tea," he said.

"So what we're saying is that they're probably unaware of what they've done, or if they are overseas visitors, not sure of how Australians ... react to these sacred sites."

The RSL says the offenders should get the strictest possible penalty.

"They looked like brainless yahoos, probably with a gutful of grog, just being stupid," NSW president of the RSL Don Rowe said earlier in the week.

It's the second time in four months the Cenotaph has been vandalised.