The ACT government introduced a bill in the Legislative Assembly to permit same-sex marriages.

The bill is expected to pass the 17-member Assembly next month with the support of all eight Labor members and Greens minister Shane Rattenbury.

But Mr Abbott said the Commonwealth had constitutional responsibility for marriage and Attorney-General George Brandis would seek advice on the ACT bill.

''The ACT is entitled to do what it can within the law,'' he said. ''And, as you know, under the constitution the Commonwealth has responsibility for marriage. The Attorney-General will be seeking advice on precisely how far that extends.''

The federal government could challenge the ACT law in the High Court of Australia or attempt to disallow it through votes in both houses of Parliament.

ACT Attorney-General Simon Corbell said it would be a tragedy if the Federal Parliament overturned an ACT same-sex marriage law. ''What we do know is that the federal government is deadlocked,'' he said. ''It would be a tragedy if they can't legislate for same-sex marriage but they can legislate to overturn same-sex marriage.''

The ACT government believed its marriage equality bill could operate alongside the federal Marriage Act because the territory law would only apply to same-sex couples, not heterosexual relationships.

Federal Labor leadership candidates Anthony Albanese and Bill Shorten both referred questions on the issue to shadow attorney-general Mark Dreyfus.

Mr Dreyfus said it was up to the Prime Minister to explain whether he would bring forward legislation to overturn the ACT bill if and when it became law. ''If he does, Labor will consider the Commonwealth bill closely, and determine whether it would be subject to a conscience vote - something Mr Abbott has always refused to grant to his MPs,'' he said. Labor has a conscience vote on same-sex marriage. Mr Albanese and Mr Shorten have both previously voted in support of proposed changes to the Federal Marriage Act to allow gay marriages.

Rodney Croome, national director of Marriage Equality Australia, said Mr Albanese and Mr Shorten should both make it clear that they would oppose any move by the federal government to overturn a territory marriage equality law.

''Although the Labor Party has a conscience vote on the issue of marriage equality, in this case it should be a binding vote because the issue is about territory self-government,'' Mr Croome said.

Mr Corbell received a standing ovation from marriage equality supporters in the Assembly's public gallery after he introduced the same-sex marriage bill.

''It is a bill that says people in a same-sex relationship are able to have their love and commitment to each other legally recognised in the same way that people in a heterosexual relationship are able to through a legally recognised marriage,'' Mr Corbell said.

The same-sex marriage law would operate in a similar way to the Federal Marriage Act. Same-sex couples from other parts of Australia and overseas would be able to marry in Canberra, but the marriages might not be recognised in their home jurisdictions.

Ministers of religion could refuse to officiate over, or make their places of worship available for, same-sex weddings.

Divorce cases would be heard in the ACT Supreme Court.

Opposition Leader Jeremy Hanson said the Canberra Liberals would not support the legislation when it is debated by the Assembly next month. ''Firstly, it's likely to be found unconstitutional, and certainly I think everybody agrees it's going to be subject to a High Court challenge,'' he said. ''Secondly, it's just simply not the job of the ACT Assembly to be determining what is clearly controversial, national social reform. For those two reasons we won't be supporting it.'' He said the Liberals had a range of views on same-sex marriage ''but what we all agree on is it shouldn't be debated by the Legislative Assembly of the ACT, which is Australia's smallest jurisdiction''.