But Mr. Turnbull said the council was “using a day that should unite Australians to divide Australians.”
The assistant minister for immigration, Alex Hawke, told the council on Wednesday that its power to conduct citizenship ceremonies would be revoked because it had breached the Australian Citizenship Ceremonies Code, a federal document that describes how such ceremonies should be conducted.
“We are committed to ensuring that citizenship is treated in the ‘noncommercial, apolitical, bipartisan and secular manner’ which the code mandates,” Mr. Hawke said in a statement.
Top officials in Yarra would not be able to preside over future ceremonies, he said, a decision that would take effect on Friday.
Mr. Hawke had earlier warned the council that it would face consequences if it did not comply with the citizenship ceremonies code.
“You must not use your ability to preside over citizenship ceremonies, or determine the dates upon which they are held, to in any way delegitimize Australia Day,” Mr. Hawke wrote in a letter to the council on Monday. “Any action would be a serious breach of the code.”
Amanda Stone, the mayor of Yarra, said the government had also accused the council of politicizing the citizenship ceremony. The code stipulates that ceremonies should not be used for political, religious or commercial purposes.
“We are certainly acting politically by not holding a ceremony on that day, but there is nothing requiring us to do that,” Ms. Stone said. “It’s touched a nerve. The people who are opposed to what we are doing identify with Australia Day as part of their own identity and feel that we are interfering and taking something away.”
Ms. Stone said the council had surveyed 300 people, including residents, businesses and visitors, before putting the issue to a vote on Tuesday night.
But some constituents have questioned the level of public comment.
The council received emails from some residents who did not support the decision. Some said it was “appalling,” and others described themselves as “dismayed.” Another wrote that he was sympathetic to the position of Indigenous people but expressed “disgust and disappointment” at the vote.
Stephen Jolly, a city councilor, said Yarra, which has a large Indigenous population, was the site of Aboriginal activism.
“When Muhammad Ali visited Australia, he specifically went to the heart of Yarra to visit the Indigenous community,” he said.
Mr. Jolly said the Indigenous community had approached the council to discuss the possibility of moving celebrations to another day.
“They came to us and said, ‘We’re up for celebrating Australia, there’s a lot of things to celebrate, but why that day? That’s the day when we had our continent taken off us and it was declared a penal colony of England. There’s got to be a better day.’”
Kate Darian-Smith, a professor at the University of Melbourne, said that every year the day raised questions about the country’s national identity and history.
The City Council of Fremantle, in Western Australia, this year suggested holding an alternative citizenship ceremony on Jan. 28 that would be more culturally inclusive, but the government condemned the proposal, Professor Darian-Smith said. The council was forced to reinstate the ceremony on Jan. 26, she said.
“Like all national days, the significance attached to Australia Day has changed over time,” Professor Darian-Smith said.