Critics of Native Title activities should come up with "hard evidence", according to Premier Steven Marshall.
Mr Marshall, who is also Aboriginal Affairs Minister, spoke in Port Pirie where he attended a trade conference last Wednesday.
He was asked by The Transcontinental whether a Royal Commission should be held into Native Title's alleged problems.
"There are always rumours, but people need to provide hard evidence," he said. "If they are going to make these accusations, then they can go through the normal investigation."
The original push for the inquiry has come from the Adnyamathanha community around Port Augusta.
They want to clarify how royalties from the Beverley uranium mine are handled by the Adnyamathanha Traditional Lands Association.
When asked about an inquiry earlier this month, the South Australian government said the Adnyamathanha reform group should take its concerns to the National Native Title Tribunal which handles such matters. The government also said its Energy and Mining Department did not collect royalties on behalf of third parties under the Mining Act, including from Beverley uranium mine run by Heathgate Resources.
"Any production payment from Heathgate Resources to the Adnyamathanha Traditional Lands Association or other third parties will be a private agreement between the parties," a spokesman said.
"Under the Royalties for Regions program, 30 per cent of revenue from mineral and petroleum royalties collected by the government is set aside for infrastructure projects that benefit the regions." Indigenous Australians Minister Ken Wyatt is believed to be following developments in South Australia involving the Adnyamathanha.
Earlier, he said the federal government had no plans for a Royal Commission into Native Title "at this time".
His office pointed to plans to increase accountability and transparency of Native Title corporations.