Prime minister Tony Abbott and senior cabinet minister Malcolm Turnbull appear to be at odds over the likelihood of a vote in federal parliament on whether to allow same sex marriage.

Mr Turnbull says it is “likely” the coalition government will allow a conscience vote on gay marriage before the next election.

Mr Abbott however, has said he was not expecting it, arguing parliament previously had rejected the idea.

“I’m not expecting any legislation to come before the parliament because when legislation came before the last parliament it was fairly decisively dealt with,” the prime minister told reporters in Sydney.

“But if legislation comes before the parliament, it will be considered by our party room in the usual way.

“It is really up to individual members of parliament to propose private member’s bills if that’s what they want.”

After the High Court’s decision to strike down ACT same-sex marriage laws, attention has now shifted back to federal parliament.

Legislation to allow gay marriage was voted down in the last parliament, with then opposition leader Tony Abbott refusing to allow his party a conscience vote.

But Mr Turnbull, a supporter of gay marriage, says that could if change if the issue is revisited in the next three years.

“I think it is likely that we will (have a free vote), but as Tony Abbott has said, it is a decision for the party room, not for him,” he told Sky News on Sunday.

“If a free vote is allowed I will certainly vote in favour of a marriage equality bill.”

Mr Turnbull said it was too early to predict whether the new parliament would back same-sex marriage legislation but Australia appeared to be lagging behind other countries.

The big change was not the composition of parliament, he said, but the international “context” in which New Zealand, Canada, South Africa and parts of the United States and the UK had legalised gay marriage.

“If you think about the countries that we are culturally closest to, they are the big English-speaking democracies,” Mr Turnbull said.

“So people of the same sex can get married in Auckland and Wellington, Toronto and Ottawa and Vancouver, in New York and Los Angeles, and Baltimore, in Cape Town, but not Australia.

“It does start to look as if we’re the ones out of step.”

Despite his support for gay marriage, the eastern Sydney MP said he would not co-sponsor a bill with Tanya Plibersek, as requested by the deputy Labor leader.

“I can’t co-sponsor a private member’s bill because I’m a member of the cabinet,” he said.