Peter Dutton hasn't committed to holding a second referendum on constitutional recognition for Indigenous people in his first term, should he win the next federal election.
The opposition leader has pledged to hold a another referendum should the upcoming October vote fail, if the coalition is returned to power.
It would change the constitution to recognise Indigenous people, but not enshrine the Indigenous voice advisory body.
Asked when the referendum would be held, Mr Dutton did not set out a date.
"You go to a referendum when you believe that that it can pass," he told the ABC's RN.
Mr Dutton said he would sit down with the Labor Party to have a “sensible conversation” about constitutional change.
The Uluru Statement from the Heart called for an Indigenous voice to be enshrined in the constitution.
Liberal frontbencher Simon Birmingham has previously flagged the possibility of holding an election and referendum at the same time, but did not specify when.
Opposition Indigenous spokeswoman Jacinta Price has refused to publicly support Mr Dutton's proposal.
Asked if she backed a second vote, Senator Price said the coalition needed to have “further discussions” but stopped short of endorsing it.
Mr Dutton insisted he had the support of his frontbencher, and reaffirmed his party's commitment to constitutional recognition.
Indigenous leaders have criticised the proposal as lacking practical measures to improve lives, which they say the voice will do.
Mr Dutton criticised Prime Minister Anthony Albanese's advocacy of the voice, when he said it lacked the support of the majority of voters.
"The prime minister has a responsibility to all Australians to act in our national interest," he said.
"If he's taking us to a point where he thinks that it can satisfy a political need for him but it's going to divide the country, I don't think that is leadership," he said.
