Debate over building a high-level nuclear waste dump is not over yet in South Australia, with Premier Jay Weatherill saying he wants a state-wide referendum on the issue.

Mr Weatherill said he was keen to restore bipartisanship with a "broad social consent secured through a state-wide referendum".

"Ultimately this is a matter for people to decide, not politicians," he said.

"If broad social consent were to be achieved through a referendum, a local Aboriginal community would also be given a final right of veto on any future facility on their land."

SA Greens leader Mark Parnell said the Government would need either four Opposition Liberals or four crossbenchers' votes in the Upper House to allow any referendum but it had neither.

Mr Weatherill's nuclear push suffered a setback this month when a citizens' jury decided against the idea.

Its report outlined concerns with the economics, along with issues of trust, safety and a lack consent, particularly from Aboriginal elders.

Mr Weatherill said 50,000 people had their say during the consultative process.

"Given that trust was at the heart of the citizens' jury's concerns, our judgment is that the best way forward is to restore that trust by putting the decision in the hands of people, not parties, not politicians," Mr Weatherill said.

Referendums in SA: 1991: Electoral redistribution (Yes)

Electoral redistribution (Yes) 1982: Daylight saving (Yes)

Daylight saving (Yes) 1970: Retail late trading (No)

Retail late trading (No) 1965: Conduct of lotteries (Yes)

Conduct of lotteries (Yes) 1911: MPs' pay rise (No)

MPs' pay rise (No) 1899: Commonwealth bill (Yes)

The citizens' jury debated the Nuclear Fuel Cycle Royal Commission report that recommended creating a high-level waste nuclear dump to store spent fuel from around the world.

Mr Weatherill said the jury process saw many non-Aboriginal people swayed by Aboriginal people both among the jurors and as guest speakers to the forums.

"If they don't want it on their lands, it is something that will not be imposed," he said.

"I wanted to make it clear to them their concerns will never be overridden by this Government or by my party."

Distrust a 'fundamental issue': Premier

Mr Weatherill said the state needed to grapple with the "fundamental issue" of distrust between Indigenous and non-Indigenous South Australians.

"This remains an issue in other developments and activities going to occur in lands that the Aboriginal people regard as their own," he said.

Dianah Mieglich was a citizens' juror who voted against continuing down the path of South Australia considering a nuclear waste facility.

She said the statement the Premier had now delivered came as no surprise to her.

"I think the posturing and the language that happened immediately after the report was handed to the Premier left lots of unanswered questions for me and I actually felt at the time that he was looking for another path to continue the conversation," she said.

She said political efforts could best be directed to other issues in the state.

"I don't believe it's going to be an easy task to get bipartisan or even multi-partisan support ... I would like to see energy put into getting multi-partisan support on a number of other issues important to our state right now," she said.

The SA Premier accused Opposition Leader Steven Marshall of withdrawing his support for a nuclear waste dump before the consultation process had been completed.

"The Government has consistently said without bipartisanship the proposal could not progress," the Premier said.

Mr Weatherill briefed the Federal Government last week about the nuclear waste issue.

He said a joint parliamentary committee was still to report and an advisory panel was yet to analyse some of the jury responses.

Mr Weatherill travelled to Finland this year to inspect a nuclear waste dumping system and said that country took 38 years to make its decision.

Conservation SA chief executive Craig Wilkins said the state's nuclear dump was "a dead plan walking".

"This will fall over through a lack of support in Parliament for a referendum, or a failed state-wide vote. Either way it is doomed," he said.

Mr Marshall said the Liberal Party's rejection of the dump was reconfirmed by a unanimous partyroom vote shortly after the Premier's public statement.