The vandalism of statues of Captain Cook and former NSW governor Lachlan Macquarie is a "cowardly criminal act" reminiscent of the Soviet dictator Joseph Stalin, Prime Minister Malcolm Turnbull says.

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".