Mr Abbott met with indigenous leaders in Canberra on Thursday, agreeing to hold the consultations on how to change the nation's founding document to include Aboriginal and Torres Strait Islander Australians.
Indigenous leader Noel Pearson told reporters the "show was back on the rails" after the prime minister changed his mind.
Before the meeting, the Prime Minister denied that he had reversed his opposition to indigenous community meetings on constitutional recognition.
"There hasn't been any about-face," he told reporters when asked by NITV News Myles Morgan why he was now open to talking about the issue.
"What we want to do is to have a unified process which certainly will involve indigenous people talking," he said.
"It will involve the wider community talking and what I want to see is not some kind of ‘them and us’ process, but a ‘we the people’ process.
"Obviously, it's important for indigenous people to have a chance to talk this through as thoroughly as possible."