Former deputy prime minister Barnaby Joyce has admitted he was wrong to label an Indigenous voice to Parliament a "third chamber", but has stopped short of supporting constitutional change because of the risk of failure.

He has instead renewed his call to radically redesign the Senate to boost representation for regional areas and First Nations peoples, saying he would put forward a private member's bill to divide each state into six regions with two senators each.

Former deputy prime minister Barnaby Joyce admitted he was wrong to label an Indigenous voice to Parliament a "third chamber". Credit:AAP

Mr Joyce was accused of misunderstanding the Uluru Statement from the Heart in 2017 when he said its key recommendation for a "First Nations Voice" would be "another chamber" of Parliament and "just won't fly" with the Australian people.

The statement called for a representative body to give Indigenous Australians an official channel for input into laws and policies affecting them. The body would be elected and enshrined in the Constitution, requiring a referendum.