Barnaby Joyce has admitted he may have been wrong to characterise a constitutionally enshrined Indigenous voice to parliament as a third chamber, apologising “unreservedly” for any “mistake”.

The apology comes despite senior figures in the Coalition government labelling the voice a third chamber as recently as last week.

The former deputy prime minister turned backbencher labelled the voice a third chamber just days after the Uluru Statement from the Heart was delivered in May 2017, a mischaracterisation that continues to dog the debate.

On Thursday, under questioning from the ABC’s Patricia Karvelas, Joyce admitted he might have got it wrong.

“If I got it wrong, I apologise. I apologise. There you go. Unreservedly,” he said. “What I do say, we’ve got – we’ve got to take this debate forward … take the debate forward in a form that succeeds. There’s no point going to a referendum with something that is not going to work.”

Joyce has been pushing for additional regional senators as a way to increase Indigenous representation without a referendum.

.@PatsKarvelas: Do you regret suggesting the Uluru Statement from the Heart proposed a third chamber? @Barnaby_Joyce: If I got it wrong then I apologise. Unreservedly. We’ve got to take this debate forward. We've got to take the debate forward in a form that succeeds #auspol pic.twitter.com/BdNY2SQVOh — ABC News (@abcnews) July 18, 2019

“The two things that won’t work: people think they’re being over-governed or it’s a motherhood statement. If it doesn’t get through, it’s a bad idea.

“But regional senators is something that will give vastly greater Indigenous representation and, even if they’re not Indigenous, they have to be very aware of the Indigenous issues, and we could do it by an act of parliament.

“I will respectfully conduct that conversation with the Indigenous leaders to see if we can get support and where we go from there.”

The mischaracterisation was repeated throughout the debate following the handing down of the Uluru statement, and was echoed by the then prime minister, Malcolm Turnbull, when announcing cabinet had rejected the proposal in October 2017.

Scott Morrison also rejected the proposal as a “third chamber” when taking over the prime ministership late last year. The home affairs minister, Peter Dutton, used the term as recently as last week while explaining why the government did not support a voice.

The actual proposal has been for an advisory board that would review any policy or legislation which would impact on First Nations people, and which could not be abolished like John Howard did with Atsic.

It would have no veto powers and would be unable to change or enter legislation into the parliament, and instead would be limited to the same recommendation powers held by current parliamentary committees, which the parliament can adopt, or reject.

The Indigenous Australians minister, Ken Wyatt, has announced plans for a referendum on Indigenous constitutional recognition within the next three years but has already cautioned First Nations leaders on what can be achieved.

Wyatt has indicated any voice to parliament may be legislated rather than constitutionally enshrined, urging advocates to be “pragmatic” about what is possible, given Australia’s history of rejecting referendums. Wyatt has also warned he will not bring the referendum to the public, if there is any hint it will not be successful.