The City of Darebin in Melbourne's north, which included suburbs of Northcote, Thornbury, Preston and Reservoir, voted on Monday night to follow the lead of neighbouring Yarra Council in moving its Australia Day events from January 26.

Emotional Indigenous community members held up an Aboriginal flag and gave councillors a standing ovation as the decision was handed down.

More than 80 people, including residents, police, security guards and the media packed into the Preston City Hall.

The meeting became heated within minutes, as some irate residents grilled councillors on why they were voting for the date change without further consultation.

One resident, Keith Coffey, accused the council of bowing to a minority, arguing only 81 people out of a population of more than 146,000, had responded to a council survey on the change of date motion.

Others said councillors were robbing migrants of their right to a citizenship ceremony in their own municipality.

Local Aboriginal woman Lidia Thorpe said Australia's colonisation had caused pain and displacement for generations of Indigenous people.

"My heart is pounding because of the hurt that has already been created in this room for us," she said.

"Australian people need to come to terms with the truth of this country for us to move forward. There needs to be an understanding of the human rights of all people. We have a public holiday for horse racing, for a football grand final, but no public holiday day to recognise the first people of this nation."

Ms Thorpe said that historically the federal government's treatment of Aboriginal people had been "appalling" but local councils like Darebin had the power to create grassroots change.

On Tuesday, Premier Daniel Andrews said Darebin Council's decision was a "great shame".

"I think you can have a celebration on January 26 of the things that are quintessentially Australian - our values, the things that we hold dear," he said.

"And you can do that in a respectful way acknowledging and honouring the contribution and the heritage of our nation and its first peoples."

Mr Andrews said he had been involved in many events that had been able to strike that appropriate balance on Australia Day.

"I think it's a great shame that others are not prepared to do the hard work to get that balance right."

A report to Darebin council said there was a surge in community support to change the date.

It said while Australia Day marked the arrival of the first British ships in 1788, it had become known as Invasion Day among many Indigenous Australians and was a day of "sorrow and mourning."

Yarra's move on Tuesday prompted a furious political backlash, with Prime Minister Malcolm Turnbull telling parliament the decision was "utterly out of step with Australian values".

He cancelled citizenship ceremonies at Yarra from Australia Day next year.

Darebin Mayor Kim Le Cerf said it was time to stop unnecessarily excluding Indigenous people on January 26.

"It cannot truly be a national day when the oldest part of our nation cannot hold it equally with the rest us," she said. "It is time to set it right."

She also rejected claims the council deliberately pushed the vote forward following the controversy surrounding Yarra.

"We are your elected representatives to make decisions on behalf of our community and that's the way representative democracy works," she said.

"Sometimes we just need to stand up for what we believe in and we believe it is harming the well-being of Aboriginal and Torres Strait Islanders."

Darebin Labor councillor Julie Williams rejected the proposal, arguing the matter should be handled by the federal government.

"Local councils should stick to rates, roads and rubbish," she said.

Councillor Lina Messina also voted against the proposal citing a lack of consultation.

Earlier this month, Assistant Immigration Minister Alex Hawke wrote to councils warning them to oblige by rules around ceremonies or else they would lose their hosting rights.

At least another two councils - Moreland and Hepburn Shire - are also debating whether to join the battle to change the date of Australia Day.

Prior to the vote on Monday evening, Yarra and Darebin councils had already arranged a joint press conference on Tuesday morning foreshadowing with almost certainty councillors would vote in favour of changing the date.

Councillors voted to replace the ceremony with a "culturally appropriate event" and to dump all references to Australia Day, including renaming its Australia Day Awards the "Darebin Community Awards".