The advocacy group spearheading the push for Indigenous recognition in the constitution is calling for the Prime Minister to urgently convene a promised meeting with Labor and Indigenous leaders on the future of the referendum.
Tony Abbott favours holding a referendum in 2017 on the 50th anniversary of the successful 1967 vote which removed a number of references that discriminated against Aboriginal people.
In March, Mr Abbott signalled his agreement to hold a meeting with Opposition Leader Bill Shorten and Indigenous representatives to discuss key issues related to constitutional change, but that meeting is yet to take place.
Recognise on Monday released a poll that suggested 75 per cent of Australians would back a yes vote if the referendum was held now.
The poll was conducted by Polity Research for Recognise in March and took responses from 2,700 voters.
To be successful the referendum would need an overall majority across the country and backing in the majority of states.
The poll, which has a 2 per cent margin of error, found that the majority of people in all states were in favour of the change.
A separate poll for Recognise of Aboriginal and Torres Strait Islander voters found 87 per cent were in favour. That poll had a sample size of 750 respondents and a 4 per cent margin of error.
Poll should give leaders confidence: Recognise
Recognise joint campaign director Tanya Hosch said the poll should spur Mr Abbott to name a date for the promised bipartisan consultations.
“This confirms that when you ask them to make this decision in a democratic vote, our fellow Australians are prepared to say yes in the sort of overwhelming numbers that would absolutely carry this referendum,” she said.
Ms Hosch said that traditionally, conservative voters were less inclined to support changes to the constitution but the poll has found 67 per cent of Coalition voters would back the changes in this case.
She also said higher levels of support were found in regional and rural areas when compared with metropolitan voters.
A specific question has not been formulated for the referendum.
A joint parliamentary committee is considering the steps that can be taken towards a successful vote and is due to hand down its report by the middle of the year.
“The research findings should give confidence to leaders as they seek agreement on the model to be put to voters. It confirms the electorate is strongly prepared to back this change,” Ms Hosch said.
A poll released by the Australian National University earlier this year found 82 per cent of respondents were either supportive or strongly supportive of constitutional change.