The ACT Legislative Assembly has passed a motion calling on the Commonwealth to amend the laws to allow same-sex marriage.

The Greens motion says the Legislative Assembly supports marriage equality, and calls for changes to the federal Marriage Act.

The Tasmanian Parliament passed a similar motion in September.

"Momentum for change continues to grow as more and more Australians agree that the time has come to amend the Marriage Act to remove the discrimination that currently exists," said Greens MLA Shane Rattenbury.

"Because of the growing support I believe we are beyond the point where the question is whether we will have marriage equality. The question now is when it will occur and I hope our motion helps to make it sooner rather than later."

Deputy Chief Minister Andrew Barr, who is openly gay, will lobby for same-sex marriage at the federal Labor Party conference next month.

He says the one remaining area of significant legal discrimination in Australia is the federal Marriage Act.

Earlier this week Prime Minister Julia Gillard, who is opposed to same-sex marriage, said she thinks Labor MPs should be given a conscience vote on gay marriage.

But Mr Barr says he does not support a conscience vote on the issue within his party.

However he says the Liberal Party should allow its members a conscience vote because that party is unlikely to adopt a binding position in support of marriage equality.

Canberra Liberals Leader Zed Seselja says that is a hypocritical stance, and he rejected the Greens motion.

He says it is not up to Parliament to grant or take away the concept of marriage.