SYDNEY (AFP) - Australian Prime Minister Tony Abbott Thursday brushed off mounting pressure for a parliamentary vote on same-sex marriage from within his conservative coalition, saying he was more focused on the economy and security.

A marriage equality bill is set to be proposed by a Liberal Party backbencher when parliament returns in August, seconded by an opposition Labor representative, with other co-sponsors from multiple parties, the Australian Broadcasting Corporation reported.

Mr Abbott, a staunch Catholic against changes to the Marriage Act, acknowledged that same-sex marriage was an "important issue" but said the private member's bill was unlikely to be debated and voted on.

"It's quite unusual for private member's bills to come on for debate and vote in the parliament," he told reporters.

"I have been in the parliament now for 21 years and there's only been from memory two or three occasions when a private member's bill has come on for debate and vote."

The push to put the issue in the spotlight came after the United States Supreme Court's recent landmark ruling legalising same-sex marriage nationwide, and Ireland's referendum in favour of gay marriage.

Mr Abbott, who has a gay sister, said his government was "absolutely focused on the things that we were elected for" such as jobs growth and securing the country against "various challenges at home and abroad".

His conservative government's official stance is opposition to gay marriage, and the Liberal Party has previously refused to let members have a conscience vote.

A lower house vote on same-sex marriage in 2012 was defeated 98 to 42 after Mr Abbott refused to allow his MPs, then in opposition, to break party lines.

Supporters of the bill hope the move will serve as a challenge to Mr Abbott to allow government MPs a free vote on an issue believed to have broad community support.

"I welcome this sign of progress," Labor leader Bill Shorten said of the plan to propose the bill. "I hope it means Tony Abbott will finally grant Liberal MPs a free vote on the legislation."

A poll last year found that support for same-sex marriage in Australia had reached a record high, with 72 per cent supporting marriage equality and about half of those strongly supporting it.

"Like millions of Australians, my first and only hope here is that we can make marriage equality a reality," Mr Shorten said.

Australia lags behind a growing number of countries that allow gay marriage, including Britain and neighbouring New Zealand.