Sydney Lord Mayor Clover Moore told Fairfax Media she had referred concerns about a statue of Governor Lachlan Macquarie to the council's Indigenous advisory panel "for their consideration and in particular their advice on how the City can most effectively play a role in progressing equality and redress past injustices".

"There have been too many people in mainstream Australia ready to make judgment on these issues without consulting Indigenous communities, and whether well-meaning or not, it's often done more harm than good," she said.

The council has already sought advice from the panel about the Captain James Cook statue, with its inscription claiming the British explorer discovered Australia, following criticism by ABC broadcaster Stan Grant.

Mr Abbott told 2GB's Ben Fordham on Wednesday that there would be "political correctness on steroids" if Mr Shorten became prime minister.

"You can just imagine all the statues of Captain Cook being taken down, all the statues of Governor Phillip being taken down."

The Macquarie statue is situated at the northern end of Hyde Park, near an inscription that begins: "He was a perfect gentleman, a Christian and supreme legislator of the human heart."

However, the statue, unveiled in 2013, is an affront to Tess Allas, the director of Indigenous programs at the UNSW Art & Design.

"I believe he should not be honoured in this way," Ms Allas said. "He ordered and sanctioned the murder of innocent people including children. How is it possible to honour such a fellow and still believe our society is a just society?"

Nor should he have a university named in his honour. "I'd love to see it renamed," Ms Allas said. "I'd love to see Macquarie Street renamed. I'd love to see the Lachlan River, Macquarie Fields, Port Macquarie, Macquarie Harbour, Macquarie Rivulet, Macquarie Pass, the Macquarie Bank, etc., etc., etc., renamed."

The curator of With Secrecy and Despatch, a 2016 exhibition that explored Macquarie's role in the killings of Indigenous people in western Sydney, Ms Allas said: "He was the one who ordered the first massacre and from that massacre instructed the offending troops to hang the victims from trees so as to "strike the greater terror" into any survivors.

"I feel sick just writing these words. What kind of mind thought of them in the first instance?"

As controversy continues in the US over the presence of statues commemorating figures such as Confederate Army general Robert E. Lee, Ms Allas said she would support any calls to remove Macquarie's statue.

An alternative to removal would be to provide more information, Ms Allas said. "The full story of Macquarie's governorship should be added to reflect his whole story."

Professor Bronwyn Carlson, the head of the Department of Indigenous Studies at Macquarie University, said Macquarie should not be celebrated with monuments and place names.

"When Australia matures and comes to terms with its brutal colonial history and its treatment of Indigenous people then everyone will see how offensive it is," she said. "If you think about Germany for a moment - you won't see monuments of Hitler, for example. You can teach history without celebrating those who ordered and participated in massacres."

NSW Greens MP David Shoebridge said many people believe the statue of Macquarie should not have been installed in Hyde Park.

"Monuments that have Captain Cook as 'discovering' Australia are clearly inaccurate," he said. "Likewise the pure celebration of Macquarie is both insensitive and incomplete. If we are going to retain historical monuments like these we can't choose to remember only some of the facts."

Henry Reynolds, honorary research professor of Aboriginal Studies at the University of Tasmania, said Macquarie had played a pivotal role in the development of the colony but added: "There is the fact that he, indeed like many of the other governors, was determined to crush Aboriginal resistance. So I'm in two minds about this."

Professor Reynolds said he believed monuments should be amended rather than torn down: "It means the monument remains and you can see what past generations thought, what was important to them, but you don't have to leave it like that forever."

Michael Organ, a former federal Greens MP and a historian at the University of Wollongong, said statues and monuments erected in Australia offered a partial view of history.

"Why are there no monuments to the Aboriginal people who fought and died as a result of the European invasion in 1788 and, more significantly, as a result of the war carried out again them by Governor Lachlan Macquarie in 1816?" he asked.