"Indigenous people become a postscript to Australian history."
Grant suggested the inscription could be changed to "he explored this territory"or that it could include mention of Australia's Aborigines, who are believed to have arrived about 60,000 years earlier.
The call was backed by Aboriginal leaders and prompted the City of Sydney's Lord Mayor to seek advice on this and on a statue of Lachlan Macquarie, a colonial governor accused of ordering a massacre of Aborigines in 1816.
But the moves have prompted fury among conservative historians, commentators and MPs. Tony Abbott, the former Prime Minister, seized on the debate to warn that a Labor Government would lead to "political correctness on steroids".
"You can just imagine all the statues of Captain Cook being taken down, all the statues of Governor [Arthur] Phillip [the founding governor of the British colony in New South Wales] being taken down," he told 2GB Radio.
Keith Windschuttle, historian and editor-in-chief of the conservative magazine Quadrant, said the inscription on the statue was "perfectly accurate" as Aborigines had discovered areas around what is now Sydney but Cook discovered the "whole entity".