Moves to remove Confederate statues and other Civil War- era symbols in the United States have renewed focus on the mistreatment of Aboriginal Australians in the colonial era and recognition of their place in the nation's history.
Prominent indigenous commentator Stan Grant this week pointed to the "damaging myth" inscribed on a Sydney statue of British explorer Captain James Cook that says he "Discovered this territory 1770".
But Turnbull said attempts to remove or alter such statues were mistaken.
"Trying to edit our history is wrong," Turnbull told Melbourne radio station 3AW.
"All of those statues, all of those monuments are part of our history and we should respect them and preserve them."
Sydney council this week referred concerns about the Cook statue to an indigenous advisory board.
The board will also examine memorials to New South Wales' colonial-era governor Lachlan Macquarie, who critics say ordered massacres of indigenous people.
The date commemorates the arrival of the country's first British settlers, but is termed "Invasion Day" by many indigenous Australians who say it marks the beginning of the decline of Aboriginal culture.
Turnbull said attempts to change the national day and alter monuments were being pushed by "fringe" leftists.
"I think the vast majority of Australians are as horrified as you and I are at the thought that we're going to go around rewriting history, editing the inscriptions on statues, deleting Australia Day," he said.
"But we can't get into this, sort of Stalinist exercise of trying to white-out or obliterate or blank-out parts of our history."
Conservative commentators in Australia have accused critics of bowing to political correctness and stoking racial friction.
Grant, the Australian Broadcasting Corporation's indigenous affairs editor, countered by saying that statues need not come down, but a deeper discussion about the country's history was required.
"There is a history in Australia of not wanting to talk about the darker parts of our shared past," he wrote this week.
They remain the most disadvantaged Australians, with higher rates of poverty, ill-health and imprisonment than any other community in the country.
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