Australia's federal government has ordered local governments to hold naturalisation ceremonies for new citizens on Australia Day amid controversy over the holiday, which some claim is offensive to the country's indigenous people.

The government is proposing that all local government bodies in Australia, typically referred to as councils, must hold induction ceremonies for new citizens on the Australia Day holiday on January 26 and the Australian Citizenship Day holiday on September 17 or have their authorisation revoked, Immigration Minister David Coleman said in an emailed statement on Sunday.

Australia Day marks the anniversary of the 1788 arrival of the first British fleet to Sydney Cove where the British flag was raised on the continent marking the start of colonisation.

Aborigines trace their lineage on the island continent back 50,000 years and for them, the date marks the start of the loss of their cultural heritage and suffering under discriminatory policies.

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The holiday has become controversial with pressure by activists to change the date of what they call "Invasion Day".

The country's 700,000 or so indigenous people track near the bottom of its 25 million citizens in almost every economic and social indicator.

Several local councils have stopped holding citizenship ceremonies on Australia Day because of concerns the date is insulting to Aborigines.

At a press conference televised by the Australian Broadcasting Corporation on Sunday, Immigration Minister Coleman said more than 100 of the country's 537 councils do not hold citizenship ceremonies on the Australia Day holiday.

However, Australian Local Government Association President David O'Loughlin said councils hold multiple citizenship ceremonies throughout the year and the majority of those who skip Australia Day do so for practical reasons.

"It's a very expensive undertaking to do a public event on a public holiday," he told Reuters on Sunday. "About two or three only moved the day for ideological reasons."

The proposed changes to the Australian Citizenship Ceremonies Code are planned for introduction by the first half of 2019, the minister's statement said. Coleman plans to write to the councils and receive feedback on the changes, the statement said.