Prime Minister Scott Morrison says the nation must embrace Australia Day "warts and all", but has called for another day to be set aside to recognise indigenous Australians.
Mr Morrison says January 26, 1778 is when "the ships turned up" in Australia.
"We can't pretend that it's some other day that it happened ... we've got to embrace it all, warts and all," he told the Nine Network on Tuesday.
But Mr Morrison believes there should be a separate day to acknowledge 60,000 years of indigenous history.
"We don't have to pull Australia Day down to actually recognise the achievements of indigenous Australians, the oldest living culture in the world," he told the Seven Network.
"The two can coexist."
The federal government has stripped a NSW council of its right to hold citizenship ceremonies, after it refused to hold them on the national holiday, opting instead for January 25.
Mr Morrison said if council's such as Byron Shire Council want to treat citizenship ceremonies like a "political football", the Commonwealth can easily go elsewhere.
"Citizenship is about the citizens, it's not about the egos of councillors," he said.
Deputy Labor leader Tanya Plibersek said the opposition also supports Australia Day remaining on January 26 and is open to the idea of an additional day to recognise indigenous Australians.
But Labor is disappointed the prime minister has flouted such a "significant idea" through the media without consultation.
"It's disrespectful," she tweeted.
"Unlike Scott Morrison, we'll consult indigenous people and our indigenous caucus about whether a proper day of recognition with an additional public holiday is a positive way forward - we're open to it."
The government last year removed the right to host citizenship ceremonies from Melbourne's City of Yarra and Darebin councils after they voted not to hold them on January 26.