The Australian Labour Party (ALP) has called for a joint referendum on indigenous recognition in its constitution and the country becoming a republic.
Anthony Albanese, former Deputy Prime Minister, on Friday suggested that the referendum should be held on Australia Day so as to create a "platform of unity."
Under Australian law, any change to the constitution requires a national referendum to return a vote strongly in favour of doing so, Xinhua news agency reported.
The date of Australia Day, currently January 26, has become increasingly contentious in recent years.
Much of Australia's indigenous population consider it a "national day of mourning", saying it celebrates the day that the country was stolen from the original Australians.
Albanese's speech came as tens of thousands of people took to the streets of Australia's major cities, protesting the date.
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He said that holding the referendum on January 26 would mean that the date became synonymous with indigenous recognition rather than the arrival of the British First Fleet in Australia in 1788, making it a day "where we can truly say that we're together as one, as a nation".
"Our nation needs to reconcile itself with the past as a precondition of creating a better future, one in which we embrace a common vision of what it means to be Australian in the 21st century.
"It would mean Australia had a day which recognised our modern history of new arrivals, our continuous history of indigenous Australians dating back now some 80,000 years and a recognition of confidence of us in a modern state," he said.
Prime Minister Malcolm Turnbull, in his Australia Day speech, said that the overwhelming majority of Australians were celebrating the holiday which marks "a story of enormous achievement".
Turnbull, who has strongly opposed any change to the date of Australia Day, said the day should include a focus on indigenous Australians.
He said: "The impact of European settlement on Aboriginal Australians was tragic; of course it was. We understand that and there are many wrongs that were done in the past, which we seek to right today."
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