Australian Prime Minister Tony Abbott said Tuesday that his coalition government would allow a constitutional referendum on gay marriage if his coalition is re-elected. Above, a gay rights activist held a placard during a rally supporting same-sex marriage in Sydney, May 31, 2015. Reuters

Australia could hold a parliamentary vote on same-sex marriage if his coalition government wins next year's general election, Australian Prime Minister Tony Abbott said Tuesday during a meeting with Parliament members over whether they should allow a constitutional referendum on a marriage equality bill. While a bill to legalize same-sex marriage is currently set to arrive in Parliament, members of the prime minister's governing Liberal-National Party have fought against the possibility of parliamentary proceedings.

"Our position going into the next election is that in a subsequent term of parliament that this is a matter that should rightly be put to the Australian people," Abbott said, as Financial Times reported. "We could have a plebiscite or constitutional referendum. We want to look at the ramifications of each option."

Roughly two-thirds of the Liberal-National coalition's 90 members of parliament (MPs) rejected a call to allow a free vote on a bill co-sponsored by Liberal and Labor MPs to legalize gay marriage. Abbott, a staunch conservative who is deeply opposed to same-sex marriage, has previously lost support among both the general public and his own party for his steadfast refusal to allow for any form of vote leading to legalization. After Ireland's vote in favor of same-sex marriage along with the U.S. Supreme Court decision, many have hoped for a shift in his position.

Abbott's concession for a constitutional referendum, or plebiscite, stands in stark contrast to comments he made in May, when he rejected a referendum in favor of a parliamentary procedure.

"Referendums are held in this country when there is a proposal to change our constitution and I don't think anyone is suggesting the constitution needs to be changed in this respect," Abbott said at the time, the Guardian reported, adding that it should instead be an issue for MPs.

A poll by the Liberal party pollsters Crosby Textor last year found that 72 percent of Australians support marriage equality, Financial Times reported.