Two senior Liberal Party MPs are split over Scott Morrison's push to celebrate indigenous people and culture on a new public holiday.
Liberal minister Ken Wyatt, an indigenous man from Western Australia, has welcomed the concept while Tony Abbott, the special envoy for indigenous affairs, is lukewarm about the idea.
The perennial debate over changing the date of Australia Day reignited after Byron Bay council in NSW tried to bring forward its annual citizenship ceremonies.
The prime minister has taken aim at the "showboating" council vote and argued shifting Australia Day would be denying the nation's history.
Mr Morrison says January 26, 1788 is when "the ships turned up" in Australia.
"You don't pretend your birthday was on another day," he told reporters in Sydney on Tuesday.
"What you do is you look at your whole life experience. Your achievements, a few scars from some mistakes and some things that you could've done better.
"As Australians, we need to reflect on all of that on Australia Day."
Instead, he has floated the idea of another day to recognise indigenous Australians.
Without nominating a specific date, Mr Morrison noted the ACT holds a public holiday on May 28 to mark the anniversary of the successful 1967 indigenous referendum.
Mr Wyatt described the idea of an indigenous day as "a great step forward" and suggested it be held during NAIDOC Week in July.
Mr Wyatt said January 26 was no longer about Australia's settlement.
"It's about us as a nation, us as a people, and the melting pot of a society that is working closely to build this nation to be a better nation," he told ABC radio.
Mr Abbott wasn't so sure.
"We've already got things like NAIDOC Week and National Sorry Day and so on, and really I think the emphasis ... is on all pulling together on Australia Day, being proud of what we've achieved," he told 2GB radio.
The Australia Day debate flared up after the Byron Shire Council was stripped of its right to hold citizenship ceremonies after deciding to host the event on January 25.
The government took similar action against Melbourne's City of Yarra and Darebin councils last year.
Deputy Labor leader Tanya Plibersek said the opposition supported Australia Day remaining on January 26 and was open to the idea of an additional day to recognise indigenous Australians.
But Ms Plibersek said it was disrespectful for the prime minister to float the idea through the media without consultation.
Australian Associated Press