A referendum on the Indigenous voice will be held between October and December and a parliamentary committee is examining the proposed wording to alter the constitution.
In a submission to the committee, Mr Abbott said the voice would introduce a "power distinction based on ancestry".
"The parliament itself is the national voice and it's where the voices of Australian citizens in all their diversity should be heard," he said.
"Win or lose, (the referendum is) likely to leave our country embittered and divided. Yet constitutional change should be unifying and bipartisan."
Mr Abbott said the process of constitutional recognition had "run off the rails" some years ago and urged the government to restart its efforts.
But former Liberal frontbencher Julian Leeser - who quit the shadow cabinet in order to support the voice - said the proposal would help shift the dial on Indigenous health, education, housing, safety and economic opportunity.
"As a Liberal, I support the idea of a voice because I believe in the dignity of the individual," he said in his submission.
"I believe better policy is made when people affected by it are consulted on that policy."
Mr Leeser made three recommendations he said would secure support from more Australians when they went to the ballot box.
He urged the government to commit to and fund the roll-out of local and regional voices in the upcoming budget, which he feared had become lost in the national debate.
He also recommended removing the clause which would allow the voice to make representations to the executive government as well as parliament, and a preamble statement recognising Aboriginal and Torres Strait Islander people as the First Peoples of Australia.
"The voice can be just as effective without 'constitutionalising' the function of making representations to the executive government," Mr Leeser said.
"Fewer Australians will vote for a proposal which creates 'room for argument' that there are constitutional problems which must be fixed by legislation."
But a submission from the Law Council of Australia said the proposed wording for the constitutional alteration was "just and legally sound".
President Luke Murphy said the voice would deliver a substantive mechanism for change and would not have a veto or law-making power.
"Australia has unfinished constitutional business and we now have the opportunity to ensure Australia's supreme law substantially recognises Aboriginal and Torres Strait Islander peoples as the original custodians of the land," he said.
The committee examining the voice proposal is due to hold its next public hearing in Perth on Friday, after previous hearings in Canberra, Orange and Cairns.
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