The Coalition appears at odds after Liberal leader Peter Dutton said he wants a referendum for Australians to decide whether ministers should be able to strip dual nationals of their citizenship if they have committed a serious crime.

Dutton floated the idea of another referendum, following the unsuccessful Indigenous Voice vote, after citizen-stripping laws were ruled unconstitutional by the High Court.

Legislation made while Dutton was minister was struck out after the court ruled it was unconstitutional for politicians to impose criminal punishment rather than the judiciary.

But the idea of a referendum brought confusion within the Coalition – and instant scorn from the government.

“This is just another thought bubble from Peter Dutton that hasn’t made it to lunchtime,” Prime Minister Anthony Albanese said on Tuesday.

“This morning you had Peter Dutton on one channel calling for a referendum and [shadow attorney-general] Michaelia Cash on another channel ruling it out. This has not been thought through. It’s not clear where this has come from.”

Later, Cash said the Coalition had “no plans” for such a vote – although it was keeping “all options on the table”. She said a referendum should be a last resort.

On the Seven Network’s Sunrise on Tuesday, Dutton said he wanted a “discussion … about whether the constitution is restrictive” about stripping citizenships.

“You can’t outlegislate the constitution,” he said.

“What we’re proposing here is a discussion about whether we have adequate laws.

“At the moment we’ve got people in our country who hate our country, who want to cause terrorist attacks.

“My opinion is that if you betray your allegiance to our country in that way you should expect to lose your citizenship.”

The Commonwealth can already apply to a court to strip a dual-national of citizenship if they have committed a serious offence and been sentenced to more than three years in jail.

The conduct has to be so serious it demonstrates they “repudiated their allegiance to Australia”, according to the Home Affairs Department’s explanation of citizenship cessation laws.

While the specifics of any referendum policy haven’t been revealed, a constitutional change giving the minister the power to strip citizenships would centralise power in the hands of that office, effectively bypassing the courts.

The Coalition has been critical of Labor spending $450 million on the 2023 Voice referendum, saying it divided the country when the money would have been better spent helping struggling Australians.

Dutton defended potentially spending hundreds of millions more during a cost-of-living crisis.

“With the Voice, it was the wrong issue for the government to put to the people,” he said.

“If we believe that we want to keep people safe, if you want to keep your kids safe – and we want to keep kids safe in our community – I don’t think you can put a price on that.

“You can deal with community safety at the same time you can make good economic decisions.”

Treasurer Jim Chalmers said it was an important issue but the “bizarre” referendum idea was an attempt by Dutton to distract from having no economic policies.

He criticised Dutton for imposing the previous laws that were thrown out by the High Court.

“Now he wants a referendum to fix his mistakes,” he told ABC Radio.

“We’ve taken a different approach; we rewrote his broken laws to create a more robust system to keep our community safe.

“He quite bizarrely wants another referendum – I don’t think this idea will last long, just like a lot of the other things that he said in an effort to try to avoid talking about the economy and his cuts.”

-with AAP