Former deputy prime minister Wayne Swan has switched his position on same-sex marriage, conceding he was "wrong" to oppose it, as new figures put Federal Parliament less than a handful of votes away from backing the landmark reform.

Australian Marriage Equality figures show that Parliament is on the brink of having enough support to legislate same-sex marriage, needing just four more votes to pass a bill in the House of Representatives. In the Senate, it is calculated a bill could pass with a majority of one.

In a sign of the growing momentum in Canberra, Mr Swan has announced he now supports same-sex marriage. The member for Lilley in Brisbane opposed same-sex marriage during the Labor years in government, voting against the reform when it came before Parliament in 2012.

Mr Swan told Fairfax Media he had found it "increasingly difficult" to reconcile his views about same-sex marriage with his support for economic and social equality.

"I've come to the conclusion that, basically, I was wrong," he said.

In the wake of a raft of Labor MPs recently declaring their support for same-sex marriage, including Chris Bowen, Ed Husic and Bernie Ripoll, AME has done a fresh calculation of support for the reform in Federal Parliament. It also says 13 unnamed Coalition MPs have switched their position to supporting same-sex marriage since the start of the year.

AME is confident there are now at least 72 lower house MPs who would vote for same-sex marriage, which is just four votes shy of the 76 required to pass a bill.

In the Senate, AME estimates same-sex marriage has 39 supporters and so would pass with a majority of one.

This is based on the assumption that Liberal MPs were allowed a free vote and includes MPs who have privately indicated they back same-sex marriage.

Australian Marriage Equality national director Rodney Croome said the small number of Coalition members publicly in favour of same-sex marriage was the "tip of an iceberg of support".

"Given a cross-party free vote, the reform has a good chance of passing," Mr Croome said.

Some Liberal MPs have been hesitant to speak out in support of same-sex marriage because the party does not have a free vote, and due to sensitivity about preselections for the next federal election.

In the lower house, AME says there are 20 supporters - from different parties - who have not declared their position publicly. In the Senate, it has identified eight private supporters, also from different parties.

Mr Croome said a lot of credit for the shift in numbers goes to "everyday Australians" who have lobbied their local MPs with personal stories.

Previous estimates from advocates and same-sex marriage backers in Canberra have played down the likelihood of the reform passing before the next election. One recent estimate had same-sex marriage as much as 20 votes away from a majority in the lower house.

There continues to be a question mark over the Liberal Party's exact position on same-sex marriage. While the party and Prime Minister Tony Abbott do not support same-sex marriage, Mr Abbott has said that the issue of a free vote would be a matter for the post-election party room.

Liberal MPs have so far passed up opportunities to discuss it in party room meetings - despite Libertarian senator David Leyonhjelm​ introducing a "freedom to marry" bill in the Senate last year.

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