A Turnbull government minister has moved to protect Captain Cook and other historic statues following a spate of vandalism.
But political opponents have criticised what they see as a return to "history wars".
Environment Minister Josh Frydenberg has asked the Australian Heritage Council to recommend how to enhance protections for the historic monuments.
Captain Cook's statue in Sydney was spray-painted with slogans including "change the date" after a renewed public debate about the appropriateness of January 26 as Australia's national day.
"We shouldn't be defacing our history," Mr Frydenberg told Sky News on Sunday.
"When we saw those criminal acts on that Captain Cook statue, the prime minister was very quick off the blocks to condemn it and to remind everyone that we shouldn't be seeking to rewrite our history."
The heritage council is expected to give the government its recommendations early next year.
Labor frontbencher Doug Cameron said the government was trying to distract from issues families genuinely cared about.
"I would have thought Frydenberg would have had more important issues on his mind than that," Senator Cameron told reporters in Canberra on Monday.
"Writing to anyone about statues I don't think is an example of leadership."
Greens senator Peter Whish-Wilson dismissed it as "just part of the government's culture wars".
"It's part of a short-term strategy to make sure they don't lose votes to the far right conservatives in this country like One Nation," he told reporters.
Crossbench senator David Leyonhjelm said Australians' concern over historic statues appeared derived from similar debates in the US.
"It's about history wars. Do we try to judge past deeds and past people by modern or contemporary standards?" he asked.
"It's a bit of a sad reflection on our political immaturity that we can't think of our own ideas on how to make a political statement."
But Liberal senator James Paterson said the minister's request of the heritage council made sense.
"They are part of our history. They are part of our heritage. These are nationally significant monuments and institutions and they should be protected too," Senator Paterson said.
"We have Bill Shorten out there saying he's going to chisel footnotes on every statue. That's just impractical and silly."
