As Mr Abbott also called on Labor leader Bill Shorten not to politicise the issue, estimates show Canberra is just one MP away from gathering enough support to a pass a same-sex marriage bill through both houses.

Labor's Anna Burke has become the latest MP to declare her support for same-sex marriage, which takes the lower house to 75 MPs in favour of same-sex marriage, based on Australian Marriage Equality's analysis. Seventy six votes are needed to pass a bill.

In the Senate, estimates have same-sex marriage passing with a majority of one.

These figures assume that Liberal MPs are given a free vote and includes MPs who have only declared their support in private.

Ms Burke's announcement comes as Mr Shorten announced he will introduce a bill to legalise same-sex marriage into the lower house next week, and in doing so, try and force the issue in the Liberal party room.

The move has angered some Liberal MPs who support same-sex marriage and do not think Labor pressure will help them secure a free vote for their side. It has also caused confusion in the Parliament, given Liberal Democrat senator David Leyonhjelm and the Greens also have same-sex marriage bills on the Senate's books.

During question time on Wednesday, Mr Shorten asked Mr Abbott if he would let his MPs have a free vote.

The Prime Minister replied that even though he could not "forsee the future", if Parliament did discuss same-sex marriage, it should be under a non-partisan banner.

"If our Parliament were to make a big decision on a matter such as this, it ought to be owned by the Parliament and not by any particular party," he said.

"I would ask the Leader of the Opposition and all members of Parliament to consider this as we ponder these subjects in the weeks and months to come."

Mr Abbott is a staunch defender of the existing marriage definition. But he has previously said it will be up to the Liberal Party to decide their position on a free vote and has conceded he is the only person in his family who is against same-sex marriage.

On Wednesday, Ms Burke revealed that she not only backs same-sex marriage but a binding vote.

The former speaker did not vote when a same-sex marriage bill last came before the House of Representatives in 2012 and was defeated.

"Marriage equality should be endorsed by our Parliament and our community, as it is a fundamental right that everyone should be equal before the law and marriage is a legally binding contract enacted under law," Ms Burke said.

"My marriage will only be enhanced by all those who seek to publicly declare their union, children will only benefit from their parents being able to publicly declare their union and our society will only be enhanced by removing discrimination."

Ms Burke polled her electorate on marriage equality in 2010, which told her "my community did not support a change to the Marriage Act". The Labor MP holds the seat of Chisholm in Melbourne's eastern suburbs.

She explained she did not put forward her own personal view at the time because she believed same-sex marriage "needs to be embraced by the community to ensure lasting equality".

Ms Burke follows similar announcements from Labor colleagues Wayne Swan, Tony Burke, Chris Bowen, Ed Husic and Joel Fitzgibbon in recent weeks.

Australian Marriage Equality said it welcomed Ms Burke's support.

"It will send a positive message to Labor members who have yet to support the reform that they should get their skates on," national director Rodney Croome said.

"By our estimation we are now just one vote short of a majority in the lower house."

Mr Croome cautioned that the news did not mean "we should rush to a vote".

"It's important that the Coalition allows a free vote for its members and that these members have a chance to have a dialogue with their electorates about the reform."