Hobart City Council is considering changing the date of its Australia Day celebrations.

The council is looking at moving its citizenship ceremony from January 26, a date that Alderman Helen Burnet says is a day of mourning for many.

“We don't want to be isolating people, it's really important in the process of reconciliation for Tasmanians that we think about how we celebrate Australia day and when we celebrate Australia Day,” she told the ABC.

Additionally, Hobart Lord Mayor Sue Hickey has successfully moved an amendment to lobby the Federal Government on the issue, despite being something of a naysayer herself.

The head of the Tasmanian Aboriginal Centre, Heather Sculthorpe, welcomed the moves.

“By Hobart and other councils setting the way like they have been, the pressure will really be on for [Premier] Will Hodgman to come out to support it would be a fantastic thing and it will make it all the quicker so that we can move on to something else more significant,” she said.

About 1,000 people attended an ‘Invasion Day’ rally on Australia Day in Hobart this year, fighting to recognise the destruction of Aboriginal society and culture since European arrival.

Ms Sculthorpe said it is really not about a date.

“It's about what do people want to celebrate,” she said.

“The issue for the Aboriginal community is, what conditions have to be met before what people feel there is something to celebrate and we're a way off from that.

“It's not about when will we celebrate Australia Day it's how do we reconcile, how do we form a proper relationship with the Aboriginal community.”