Earlier this year, Ms Carli-Hannan and other councillors voted to keep citizenship ceremonies on January 26, a decision that was upheld at Wednesday night's meeting.
But it is termed "Invasion Day" by many indigenous Australians who say it marks the beginning of the decline of Aboriginal culture.
Moreland has also said it would support the "change the date" push, a campaign to change the date of Australian Day from January 26, which Indigenous Australians say represents the landing of the first European Australians and thus the beginning of oppression and the killing of their ancestors.
Moreland City Council voted on Wednesday night to drop all references to January 26 as Australia Day out of respect for Aboriginal people.
A majority of Moreland councillors voted to drop all references to Australia Day, although it will continue to hold citizenship ceremonies on 26 January.
"It would be like celebrating the Nazi Holocaust", Socialist Alliance councillor Sue Bolton said at the meeting.
Moreland City Council will join other councils in pushing the country's lawmakers to change the date.
"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 Turnbull Government strongly condemns comparisons of Australia Day with the Nazi Holocaust as deeply offensive to all Australians", he said.
"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, according to the ABC.
Moreland will retain its right to administer citizenship but Mr Hawke said the government would "consider the Moreland motion and the nature of the public debate and consider further action as appropriate".
But Greens councillor Samantha Ratnam said she was "proud of council for taking this step". January 26 marks the day European colonists settled in Australia in 1788, a date which marks dispossession of and violence toward Indigenous Australians.
The annual holiday, on Jan 26, commemorates the arrival of the country's first British settlers in 1788 and is a time when citizenship ceremonies are held.
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.
"How dare you actually take away Australia Day".