The statues in Sydney's Hyde Park were spray-painted with the words "Change the date" and "No pride in genocide" in the early hours of Saturday, references to the controversy over celebrating Australia Day on January 26.

NSW Police have released images of a man they want to speak to, described as being of Caucasian appearance with a full beard, wearing black sunglasses, khaki-coloured jacket with a red shirt or scarf underneath, black track pants and brown boots.

In a long and passionate Facebook post, Mr Turnbull said the graffiti was "part of a deeply disturbing and totalitarian campaign to not just challenge our history but to deny it and obliterate it".

"This is what Stalin did," he wrote. "When he fell out with his henchmen he didn't just execute them, they were removed from all official photographs - they became non-persons, banished not just from life's mortal coil but from memory and history itself."

Mr Turnbull said defacing statues of British colonial explorers and governors was "not much better than that", and was an attempt to erase history and the perspective of a point in time.

"Old histories should not be burned, any more than old statues should be torn down," he wrote. "Rather they should be challenged and complemented by new histories, fresh evidence and modern monuments."

For example, ancient Roman monuments depicting slaves shackled to chariots did not mean modern-day Italians endorsed slavery, the Prime Minister wrote.

He conceded there were "many dark chapters of injustice, hardship and cruelty" in Australian history, "none crueller or more unjust than the dispossession of our first Australians".

But "we do not advance the clear-eyed telling of the truth as we see it today, by trying to obliterate the reality of the different perspectives of times past", Mr Turnbull said.

"A free society debates its history, it does not deny it. It writes new books, it does not burn old ones. It builds new monuments as it preserves old ones."

Other Turnbull government ministers reacted angrily to the vandalism on Saturday, including Treasurer Scott Morrison, who called it "a bloody disgrace" and "an insult to all fair-minded Australians".

"This divisive BS political grandstanding and vandalism does nothing but indulge the egos of the perpetrators," Mr Morrison wrote on Facebook. "It is an exercise in pure vanity. Grow up, you're not helping anyone or anything."

Indigenous journalist Stan Grant, who has been at the centre of debate surrounding the statues, said the vandalism was "appalling and disgraceful".

Asked about the issue at a press conference in Perth, Finance Minister Mathias Cormann said the graffiti was "outrageous" and "sadly part of a left-wing agenda that is taking hold".

He said the Turnbull government stood with "the silent majority" of Australians who want to maintain Australia Day on January 26, the date the First Fleet arrived at Port Jackson in 1788.

"Nobody should think it is a good idea to edit our history," Senator Cormann said. "We stand with the many good Australians who want to continue to celebrate everything that is great about Australia."

NSW Police acting Inspector Peter Northey said police supported the right to protest but "defacing public property is unacceptable and is criminal".