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.