After two Melbourne councils voted to scrap formal Australia Day celebrations, two councils in New South Wales are considering similar changes.

The Lismore and Bellingen Shire councils, both in northern NSW, say they are consulting their local Indigenous communities about finding the best way to approach January 26.

Dominic King, Mayor of Bellingen Shire Council, just south of Coffs Harbour, said the council was aware of community concerns that Australia Day represented a celebration of "deep hurt" for many people.

"We have initiated discussions with both Gumbaynggirr representatives and the shire's Australia Day Committee about these concerns and will continue that process before taking any specific actions," King said in a statement.

On August 8, Lismore Council voted to explore dates better suited to hosting Australia Day citizenship ceremonies and to work towards more culturally inclusive celebrations.

Lismore (south-east of Byron Bay) has sent the motion to its Aboriginal Advisory Group for support and further recommendations.

Lismore city councillor Vanessa Ekins said in a statement the Aboriginal Advisory Group supported the council's proposal to write to the prime minister and state politicians to call for a change in the date of Australia Day.

"Our decision is the start of our conversation with our community about how we can more meaningfully celebrate being Australian," councillor Ekins said.

Both Yarra and Darebin councils in inner Melbourne decided to stop conducting citizenship ceremonies on Australia Day. The councils also voted to drop Australia Day from the name of their community awards and to change the date these are given out.

The federal government responded by taking away both Yarra and Darebin Councils' ability to host citizenship ceremonies at any time during year.