Prime Minister Malcolm Turnbull has condemned the "change the date" slogans painted on statues of colonial figures including Captain Cook in Sydney's Hyde Park, saying those responsible are part of a campaign to "obliterate" Australia's history.

The PM posted a lengthy message on his Facebook page, after several monuments were painted with anti-Australia Day messages overnight.

New South Wales Police have launched an investigation as Mr Turnbull compared the actions of rewriting history as being akin to measures taken in Soviet Russia.

In Hyde Park, "change the date" and "no pride in genocide" was painted on a statue of Captain Cook, the British explorer who is credited with the first European contact with Australia's East coast in 1770.

Monuments to Queen Victoria and Major General Lachlan Macquarie, a prominent former NSW Governor, were also targeted.

"Today's vandalism of statues of James Cook and Lachlan Macquarie is a cowardly criminal act and I hope the police swiftly find those responsible and bring them to justice," Turnbull's post read.

"But it is also 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. 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.

Sorry, this video has expired Stan Grant says there needs to be a discussion about our history

"Tearing down or defacing statues of our colonial era explorers and governors is not much better than that."

January 26 has been in the headlines recently, with the date's significance and relevance in contemporary Australia under the microscope after two Melbourne councils voted to move celebrations and citizenship ceremonies from January 26.

Meanwhile, statues of historical figures have been a particularly divisive issue in America, where Confederate monuments have been the scene of protests in the past month.

Acting Inspector Peter Northey said police learnt about the graffiti after receiving a phone call at about 7:00am.

"Police responded straight away and have found a number of tags, and also graffiti relating to requests to change dates and other accusations," he said.

"At this stage, police have been provided with CCTV showing one person.

"We're currently very early in the investigation and still trying to identify who that person may be."