A series of community conferences will be held to deal with the issue of indigenous recognition in the constitution.
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Prime Minister Tony Abbott and Opposition Leader Bill Shorten on Monday met with indigenous leaders in Sydney to discuss a possible referendum in 2017.
"I'm confident the time is right to move down this path," Mr Abbott told reporters.
The prime minister said the community conferences could start in September, subject to party room approval by both the coalition and Labor.
He hopes a consensus on how the constitution could be changed will crystallise by the middle of 2016.
Mr Abbott acknowledged that would leave a tight deadline for his preferred May 2017 referendum date.
"We are good enough, big enough and brave enough to do this but it is important that we get it right," he said.
Mr Abbott said Monday's meeting had been a great discussion conducted in a spirit of generosity.
"What we now need to do is end that echoing silence in our constitution - the omission of indigenous people from our constitution."
Mr Abbott said he was open to the idea of a constitutional convention at the end of 2016 or early 2017.
He declined to say whether he believed the constitution was racist.
"The whole objective is not to be them-and-us but to be one people at the end of this process," he said.
Opposition Leader Bill Shorten said the constitution should recognise all Australians.
"There needs to be compromise ... everyone needs to give a little ground to update Australia's birth certificate," he told reporters.
Greens Senator Rachel Siewert said the party was disappointed it had not been invited to participate in the meeting given constitutional recognition for indigenous people was one of its core policies.
"Of course I'm disappointed that the Greens weren't there," Senator Siewert told reporters in Perth.
"To achieve constitutional recognition, we need to have a multi-party approach.
"We now have three major parties. The Greens need and should have been there at the table."
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