Paul Keating has backed a treaty with Aboriginal and Torres Strait Islander people, describing it as the "unfinished business of the nation" and suggesting it could precede Indigenous recognition in the constitution.

The former prime minister also says he would back any move by Malcolm Turnbull to revive the minimalist model for an Australian republic that both men crafted in the early 1990s, conceding this might be the "last and best opportunity" to secure the model.

In an exclusive interview with Fairfax Media, Mr Keating says the push for Indigenous constitutional recognition has lost direction and needs to be given shape and form "by someone who believes in a treaty, someone who believes that the Aboriginal peoples need to be dealt with as a nation".

His comments come as new Prime Minister Malcolm Turnbull is being urged to re-set the relationship with Indigenous Australia and adopt a different approach to Tony Abbott.