Australian voters are positive about recognising Indigenous Australians in the constitution and establishing a voice to parliament, according to polling by Essential. A majority also supports a treaty with Indigenous Australians, according to research undertaken late last month to coincide with Naidoc week.

A strong majority of a sample of 1,097 respondents (70%) supports constitutional recognition, with 33% of that cohort of the view that achieving the change is a priority while 37% support the change but don’t nominate it as a high priority. A further 18% say they don’t support that change and 12% say they aren’t sure.

There was majority support for recognition across partisan lines, with 52% of Coalition voters in favour, 68% of Labor voters, 75% of Green voters, and 50% of the voters indicating they vote for someone other than the major parties. Support and opposition to recognition has remained relatively constant in Essential’s research since 2014.

Moderate Coalition MPs say they will 'walk with Ken' on Indigenous recognition Read more

The voice to parliament, a proposal that originated from the Uluru Statement from the Heart, was supported by 66% of the group polled, with 29% saying that reform should be a priority and 37% saying it should happen but it wasn’t a high priority, while 21% of the sample was opposed and 13% weren’t sure of their view.

There was also majority support (59%) for a treaty. Around a quarter of people (26%) thought achieving a treaty was a priority, 33% were supportive but indicated the change wasn’t a high priority, 25% opposed the change and 16% weren’t sure.

Support for all of these proposals advancing reconciliation with Indigenous Australians was higher than community support for Australia becoming a republic, which was 43% in this survey.

But Australians expressed the highest level of support for practical measures, with 74% of the sample in favour of governments meeting their closing the gap targets. Of that group, 36% said narrowing the gap in outcomes between Indigenous and non-Indigenous Australians was a priority and 38% supported the idea but argued it wasn’t a high priority, while 15% opposed the idea and 12% were undecided.

Voters were also asked for their perceptions about whether the standard of living had improved for Indigenous Australians over the past 10 years. Nearly half the sample (46%) believed that some progress had been made over the decade. Over a third said they thought things had remained the same and 8% believed conditions had deteriorated.

The Morrison government this week has reopened debate about constitutional recognition and the voice to parliament, with the minister for Indigenous Australians, Ken Wyatt, the first Indigenous person to hold the portfolio, promising to work towards holding a referendum on recognition within three years.

The articulation of a timetable follows a meeting between Scott Morrison and Anthony Albanese last week in an effort to find an initial consensus. But while unveiling the three-year timetable, Wyatt made it clear he won’t stick to it if the necessary referendum to change the constitution looks set to fail.

Wyatt used a speech to the National Press Club on Wednesday to signal he wanted to persist with creating some model of the voice from the Uluru statement, but he indicated it might be legislated, rather than enshrined in the constitution, which was the position outlined in the Uluru process.

He said he wanted to co-design the voice model but, when pressed for detail, he indicated it could be a structure enmeshing existing state and federal representative bodies that would provide advice to the parliament. Anticipating internal pushback within the government, he counselled fellow Indigenous leaders to be “pragmatic” about what could be achieved.

Conservatives have already signalled they would have problems with enshrining a voice to parliament in the constitution.

The conservative MP Craig Kelly told Guardian Australia if Wyatt wanted to pursue “words in the constitution that don’t really mean anything, that are symbolic, then that’s fine”. But if the proposal included an idea like the “First Nations voice” set out in the Uluru Statement from the Heart then that was unacceptable to him, and he predicted it would be unacceptable to like-minded Coalition colleagues. “I think that idea is divisive.”

While conservatives have expressed the objections they have long expressed towards change, moderates have endorsed Wyatt’s proposal. The Liberal MP John Alexander said: “Only by walking together and engaging can we uncover pathways to a better future, I’m with Ken on this, he has my full support for the process he has initiated and I hope it can conclude with a successful referendum vote and form of ‘voice’ we can all be proud of.”

While Labor has indicated it will try to offer the proposal bipartisanship, the key Indigenous spokespeople in the opposition have indicated there has to be ambition in the reforms taken forward.

Labor’s Pat Dodson said in an opinion piece for the Sydney Morning Herald and the Age: “We either deliver the Uluru statement from the heart in full or continue down the failed path of soft reconciliation measures – making white folks feel like they are doing something good for blackfellas and yet doing nothing to heal the nation’s wounds and achieving unity and respect.”