South Australian Premier Jay Weatherill wants a state-wide referendum on a high level nuclear waste dump.

The state’s Nuclear Fuel Cycle Royal Commission earlier this year recommended creating a high-level waste nuclear dump to store spent fuel from around the world.

But the nuclear push has been set back this month by a citizens' jury that came out against the idea.

Mr Weatherill says he wants 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.”

Reports say the Government would need either four Opposition Liberals or four crossbenchers' votes in the Upper House to allow a referendum, but it is unclear whther that support exists.

Still, the Premier says 50,000 people already 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.

The citizens’ jury was swayed by Aboriginal figures both among the jurors and appearing as guest speakers.

The jury’s report was concerned with issues of trust, safety and a lack consent, particularly from Aboriginal elders.

“If they don't want it on their lands, it is something that will not be imposed,” Mr Weatherill said.

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

“This remains an issue in other developments and activities going to occur in lands that the Aboriginal people regard as their own.”

Mr Weatherill has briefed the Federal Government about the nuclear waste issue, a joint parliamentary committee is due to report soon and an advisory panel has been set up to analyse some of the jury responses.