Australian Prime Minister John Howard has pledged to hold a referendum on changing the constitution to recognise indigenous Australians, if re-elected.
Many Aboriginal leaders want a formal apology
He says the distinctiveness of people's identity and their rights to preserve their heritage should be acknowledged.
Mr Howard admitted struggling with the issue of indigenous reconciliation during his 11 years in power.
He said the vote would take place within 18 months of an election, which is expected within months.
As Mr Howard heads towards the election - which many expect him to lose - his offer is a surprise new departure in government policy, says the BBC's Nick Bryant in Sydney.
The national referendum would ask whether a statement of reconciliation should be incorporated into the preamble of the constitution.
"If I am re-elected, I will put to the Australian people within 18 months a referendum to formally recognise indigenous Australians in our constitution - their history as the first inhabitants of our country, their unique heritage of language and culture and their special, though not separate, place within a reconciled, indivisible nation," he said.
Mr Howard has long argued that practical measures are more important than symbolic gestures in addressing indigenous concerns, so this speech marks a major shift in his thinking, our correspondent says.
But he still thinks that a collective national apology for past injustices would reinforce what he described as a culture of victimhood and therefore be a retrograde step.
Many Aboriginal leaders have already criticised the speech in Sydney, saying that tinkering with the constitution means nothing and that only a formal apology will suffice.