A third Melbourne council will dump official Australia Day celebrations, with one councillor calling the day "grossly insensitive".
But Moreland City Council will continue to hold citizenship ceremonies on the date to avoid losing its right to host them altogether.
The inner-north Melbourne council voted in favour of dropping all references to Australia Day and to join the push to change the date on Wednesday night.
Socialist Alliance councillor Sue Bolton said hosting ceremonies and events on January 26 was "grossly insensitive" to indigenous people.
"It would be like celebrating the Nazi holocaust," Ms Bolton said in the meeting on Wednesday.
Another councillor, John Kavanagh, did not support the move and said it was a decision for the federal government to make.
The federal government last month stripped Yarra and Darebin councils of their right to host citizenship ceremonies after successful votes to shift them to another day.
Prime Minister Malcolm Turnbull last month described Yarra City Council's decision to change the way it commemorates the day was "utterly out of step" with Australian values.
"On Australia Day, we recognise the greatness of our achievement as Australians," Mr Turnbull said in parliament.
"To change the date would be to turn our back on Australian values".
Moreland in 2015 moved its annual citizen awards ceremony to October.
The Australia Citizenship Ceremonies Code says local councils should hold ceremonies every two to three months and notes that Australia Day - along with Australian Citizenship Day on September 17 - are "significant days" in the calendar when "local governments and community organisations can play an important role" in raising awareness of citizenship.