Melbourne councils dumping Australia Day celebrations are being extreme and divisive, and comparing the history of the date to the Holocaust is offensive, the Federal Government says.

Moreland City Council last night became the third suburban Melbourne local government to scrap its January 26 celebrations — but it voted to retain its citizenship ceremony on the date.

It, along with nearby Darebin and Yarra councils, argues the date is offensive and inappropriate as it marks the beginning of what they call the "invasion" and "oppression" of Aboriginal and Torres Strait Islander people at the hands of the British.

"It would be like celebrating the Nazi Holocaust," Socialist Alliance councillor Sue Bolton said at the meeting.

The Turnbull Government, which has strongly criticised the decision by the councils, today said that comparison was offensive.

Councillor Sue Bolton wore the colours of the Aboriginal flag at the meeting. ( Facebook: Moreland City Council )

"The Government absolutely rejects the extreme and divisive nature of the discussion Greens and Socialist Councillors are promoting," Assistant Minister for Immigration and Border Protection Alex Hawke said in a statement.

"The Turnbull Government strongly condemns comparisons of Australia Day with the Nazi Holocaust as deeply offensive to all Australians.

"Ratepayers of Moreland, who have not been consulted and who did not sign up to dumping Australia Day, have every right to feel ashamed and angered by this divisive move."

The council could face further action from Commonwealth, which has stripped Darebin and Yarra councils of their right to host citizenship ceremonies.

Greens councillor and deputy mayor Samantha Ratnam told the meeting the decision was not about erasing history but acknowledging all of Australia's past.

"Thousands of Australians like me want to celebrate Australia Day, just not on a day that's so painful for others," she said.

Moreland Mayor Helen Davidson (L) presided over the vote. ( Facebook: Moreland City Council )

There was mixed response on social media to Moreland's decision, with some critics saying they should no longer be expected to pay rates.

People posted photos of Australian flags on Facebook showing their displeasure, while others wrote abuse.

Those in favour thanked councillors for making the "brave" decision.

Some questioned what they said was a lack of consultation with the community before the decision was made.

In a point of difference to Yarra and Darebin, Moreland narrowly voted to reaffirm its commitment to hosting a citizenship ceremony on January 26.

Mr Hawke said the Government was considering what action to take against Moreland.

"The Government will consider Moreland council's motion and the nature of the public debate and consider further action as appropriate," he said.