Hobart City Council has unanimously decided to fly the rainbow pride flag on the HCC building until same-sex marriage is legalised.

The decision was made at a council meeting last night, with the move designed to fit the council's social inclusion strategy, which has been in place since 2014.

The flag, which represents the LGBTI community, will fly on the HCC building on the corner of Elizabeth and Davey streets from today.

Lord Mayor Sue Hickey said the council had always prioritised social issues.

"Hobart City Council has always had a huge social conscience and we've exhibited that on a numerous occasions," she said.

"We've also written as a council, all 12 of us, to the Prime Minister asking for a push for marriage equality as soon as possible.

"We want to signify that the Hobart City Council is very supportive of social inclusion."

Alderman Hickey said flying the flag was in line with a number of other council activities around marriage equality, including the 2015 unanimous vote in support of same-sex marriage.

"It's very much about the social inclusion strategy," she said.

"We'd just like to focus on the fundamental right of every individual to have an opportunity to participate equally whether it's socially, culturally, economically, physically or politically in society.

"We just don't believe in excluding someone based on their sexual orientation."

'We look after our community'

Alderman Hickey said she expected some backlash, particularly from Senator Eric Abetz, but thought the broader community would be supportive.

"No doubt Senator Abetz will have something to say on the matter, but you've got the Prime Minster saying he will vote Yes," she said.

"I think the general public are horrified that we're going to spend $122 million on a postal vote that's non-binding that could be flawed."

Senator Abetz has criticised the council's social stances in the past, telling them to focus on "roads, rates and rubbish".

Alderman Hickey rejected the idea that councils should not adopt a social agenda.

"We are the third tier of government and we're not just roads, rates and rubbish. We are there for our community, every single one of them," she said.

"We look after elderly, we look after disability, we look after homelessness, we look after youth at risk, we look after migrants and we look after LGBTI.

"The social inclusion strategy is very much a part of the work we do, and that's what people have got to get into their heads."