However, it remains unclear if the recently elected government will allocate sufficient time for private member's bills in the parliamentary schedule. Greens senator Sarah Hanson-Young said she was working with sympathetic MPs from the two main parties and hoped to have a jointly sponsored bill initiated in the Senate, where its chances were best. Mr Turnbull predicted the Liberal Party would be inclined to drop its previous approach of binding its frontbench in favour of allowing all MPs, including cabinet members, to vote in the Parliament, each according to their conscience. ''I think it is reasonably likely that there will be a free - the Coalition party room will make the decision, as Tony Abbott has said - that there will be a free vote from the Coalition, and presumably from the Labor Party as well,'' he said. Despite a late switch in favour of legalising same-sex marriage by former prime minister Kevin Rudd, before the election Mr Abbott would go only as far as allowing his party room to decide the procedural question.

Like many Christian MPs on both sides of politics, Mr Abbott remains personally opposed, even though his sister, Christine Forster, is eager for law reform to allow her to marry. The prospect of a free vote has raised such hopes but Mr Turnbull cautioned it was no guarantee of success, suggesting that even if Liberals had voted freely when the matter last came up there may have been too few Labor and Coalition MPs for a majority, especially in the lower house. ''But my view, as you know, is that we should have a free vote, and if we do agree to have a free vote, I will vote in favour of same-sex marriage,'' he told Ten's Meet the Press. Several Liberals contacted on Sunday backed the move even if, in some cases, they were not inclined to support change to the Commonwealth Marriage Act. Others were more circumspect, with Sydney MP Paul Fletcher responding that he would first want to see details of the proposed bill and then would seek the views of his Bradfield constituents.

Among those thought to favour a free vote, despite backing the current definition of marriage, is Treasurer Joe Hockey. Mr Hockey has made his opposition known, arguing that it is in the best interests of children to be raised by a mother and a father. Another Liberal, Josh Frydenberg, said marriage was just the kind of matter on which people with strong views should be given free expression. ''While I support the status quo, I also support a conscience vote, acknowledging the passionate views on this issue by those for and against,'' he told Fairfax Media. Senator Hanson-Young said the best hope for change was through broad cross-party support.

Loading She said she had spoken in recent weeks with Liberal and Labor MPs but declined to ''drop names'' because it was up to them to come forward if they so wished. A bill to establish equality was rejected in September 2012 by a decisive 42-to-98 margin in the House of Representatives, but the vote was much closer in the Senate.