The City of Darebin on Monday night voted to stop holding citizenship ceremonies on Australia Day.

It also voted to refer to Australia Day as January 26 and rename its Australia Day awards as the "Darebin Community Awards".

The council is the second local government area to ban the ceremony, following the controversial lead of the neighbouring Yarra Council.

Assistant Immigration Minister Alex Hawke on Tuesday banned the council from conducting citizenship ceremonies.

"They were warned well in advance that politicising citizenship ceremonies would not be tolerated," Mr Hawke said.

Darebin Council, in Melbourne's north, takes in the suburbs of Northcote, Thornbury, Preston and Reservoir.

It said its decision to replace citizenship ceremonies on January 26 with "more culturally appropriate" activities was about "compassion and empathy to the Aboriginal and Torres Strait Islander people".

Darebin mayor Kim Le Cerf said on Tuesday night she was disappointed at Mr Hawke's action.

The council holds up to eight citizenship ceremonies every year and more than 80 per cent of new citizens already attend a ceremony on a day other than January 26, she said.

"It's ironic that the prime minister has said changing the date is a national debate we need to have, yet his government appears to be working to silence it by punishing councils for taking a stand in support of their Indigenous communities," she said.

Darebin council's decision follows a vote at Yarra Council last week to stop referring to January 26 as Australia Day and cease holding any citizenship ceremonies on that day from 2018.

Mr Hawke had previously threatened that he would strip Darebin and other "Greens-dominated councils" of their power to hold citizenship ceremonies if the events were used to make a political statement.

Under the Australian Citizenship Ceremonies Code, citizenship ceremonies must be "non-commercial, apolitical, bipartisan and secular".

The move by both councils has sparked debate about the role of local councils beyond roads, rates and rubbish.

Councils are given guidelines on how to conduct citizenship ceremonies on behalf of the federal government.

A public policy expert said on Tuesday the councils had simply exercised their freedom to determine the dates of those ceremonies.

Professor Roberta Ryan, director of the Institute for Public Policy and Governance at Sydney's University of Technology, said councils could do what they wanted in relation to awards or naming things.

"Reflecting the views of local communities and advocating their views to other levels of government is actually the role of local government as well as ... providing services," she said.

"I really do think the outrage is about people not liking what councils are saying ... and what these councils are saying is 'Australia Day is 'Invasion Day' for Aboriginal people and we don't want to be a part of it'."

But Professor Ryan said councils needed to consult with both affected parties and non-affected parties before purporting to speak on ratepayers' behalf.

"This is the step you have to take if you don't want to be subject to the criticisms."

Victorian Premier Daniel Andrews called Darebin's decision a "great shame", and Liberal Senator Eric Abetz accused the council of being out of touch.

But Darebin Council said it consulted with 27 advisory committees and the Indigenous community to make its decision.

Only 81 ratepayers responded to a council survey before the vote, and the non-Indigenous respondents "overwhelmingly" said it was not for them to decide, Cr Le Cerf said.

Speaking where an agreement was struck between a group of Wurundjeri elders and one of Melbourne's founders, John Batman - next to Merri Creek in Northcote - Cr Le Cerf rebuffed criticisms that ratepayers were not sufficiently consulted on the change.

She said it was "too important" to be subject to an opinion poll.

"Local government has a longstanding commitment to advocating on behalf of our community to other levels of government," she said.

"In 1902 they were very active in the pushing for women to get the right to vote and when there are issues of great social importance, we think we have a role to play.

"We are the closest level of government to the community, we know what the sentiment is in the community, and we will voice that."

Other councils are also reconsidering their Australia Day practices.

Mayor of Hepburn, Sebastian Klein, said its ratepayers would have 28 days to respond to a report on how the council should approach reconciliation, including how to celebrate Australia Day.

Cr Klein said the issue of citizenship ceremonies was yet to be discussed by the council, which covers the towns of Daylesford and Creswick.

"The bigger issue is really about the date we celebrate our national identity," Cr Klein said.

The City of Moreland, which takes in suburbs including Brunswick and Coburg, rejected a motion to move citizenship ceremonies from Australia Day in June.