Opposition Leader Peter Dutton has denied his repeated questioning about further details surrounding the Indigenous voice to parliament is undermining the proposal.

As the Greens formally back in their party’s support for the upcoming referendum proposal, Mr Dutton said he was looking to seek further assurances from the government the voice would improve the situation for Indigenous communities on the ground.

While Mr Dutton said a majority of Australians wanted to see the situation improve for Indigenous people, there was still confusion about the voice.

“People … want to do the right thing, but don’t understand what it is the government’s proposing,” he told ABC Radio on Tuesday.

“What would give people more assurance is if there is a bill that can explain how it’s going to work, because there are different models as well.”

Mr Dutton said he wanted to find a bipartisan position for public policy on the voice, but hit back at claims he was lowering public confidence on the issue.

“(Bipartisanship) would be the best approach but it’s frustrating when circumstances like we’re seeing in Alice Springs are brought to the attention of the government and nothing happens for months and months,” he said.

“There are models that people who might be in the sort of undecided column at the moment would cross over to support the voice if they understood it properly.”

While junior coalition party the Nationals have already outlined they would not be backing the voice, the Liberals have not put forward a formal stance.

Greens leader Adam Bandt said the party would be a united front in backing the voice, after the party room formally backed the voice referendum at a meeting on Monday.

The decision follows outspoken senator Lidia Thorpe’s decision to quit the party due to her concerns with the voice proposal.

The minor party had delayed officially backing the proposal, saying it wanted all aspects of the Uluru statement from the heart – including treaty – to be implemented.

“All Greens MPs will be campaigning for the referendum to succeed. It’s going to be an important opportunity for the country to take another step towards First Nations justice,” he told ABC TV on Tuesday.

“It was a consensus decision, and there was no dissent to it, we’re all going to be campaigning for it.”

Mr Bandt said the party had been speaking to the government for several months on ensuring all elements of the Uluru Statement from the Heart, which includes a treaty, were implemented.

“The Greens’ preference would be to see treaty first. We think that would be important,” he said.

“We want the referendum to succeed, we want First Nations justice and we want truth and treaty as well as voice.”