A second referendum to recognise Indigenous people in the constitution could be held at the same time as a future federal election.
Opposition Leader Peter Dutton has committed to holding a second referendum should the upcoming vote fail and the coalition is returned to power.
That referendum would change the constitution to recognise Aboriginal and Torres Strait Islanders, but not enshrine the Indigenous voice advisory body.
Liberal frontbencher Simon Birmingham flagged the possibility of holding an election and referendum at the same time.
"You'd want it to occur where it could then be conducted alongside a future election or the like, in a truly nationally unifying way, but without the need to conduct a separate national ballot," he told reporters in Canberra on Tuesday.
"But they're all decisions that you would work through in due course."
The referendum is due to cost about $450 million - the same as a standard federal election.
But holding them simultaneously would reduce the cost.
The Uluru Statement from the Heart called for a voice to be enshrined in the constitution in recognition of Aboriginal and Torres Strait Islanders being the first peoples of Australia.
Prime Minister Anthony Albanese told a Labor caucus meeting on Tuesday the decision by the coalition to back a second referendum was "absurd".
"(Mr Dutton) thinks we’re spending too much time on the issue, but wants to continue the debate for years,” Mr Albanese told colleagues.
He said changing the constitution was hard, but so was winning a seat from an opposition at a by-election which the government achieved in April for the first time since 1920.
"We have an opportunity to declare to the world that we are a mature nation that can come to terms with its history," Mr Albanese said.
The prime minister told parliament Mr Dutton wanted to defeat the referendum "for political reasons".
"He (Mr Dutton) wants to see Indigenous people, he just doesn't want them to be heard," Mr Albanese said.