Gay marriage in Australia is a matter for the federal parliament rather than a popular vote, Tony Abbott believes.
Nevertheless some MPs, including from the prime minister's own back bench, are pushing for a referendum after Ireland voted overwhelmingly in favour of allowing same-sex marriage in a historic referendum on Saturday.
"Referendums are held in this country where there's a proposal to change the constitution," Mr Abbott told reporters in Brisbane on Sunday.
"I don't think anyone's suggesting that the constitution needs to be changed in this respect."
Liberal backbencher Zed Seselja says he doesn't support gay marriage, but the question should be put to the people.
"If you are going to make such a fundamental change it should go to a referendum," he told ABC television.
Independent senator for Tasmania Jacqui Lambie doesn't support gay marriage either but backs a referendum on it.
Her fellow crossbencher Glenn Lazarus also wants the matter to go to the public and South Australian independent Nick Xenophon says he'd support a referendum if that was a "circuit breaker".
"I think the best approach is that there be a conscience vote in the parliament ... after all it has been an election issue," Senator Xenophon told Sky News.
Should a bill to legalise same-sex marriage come before parliament, the coalition party room would decide whether government MPs could vote freely on the matter.
"It's up to members of parliament who are eager for change to decide whether they want to bring it forward," Mr Abbott said.
The Greens have legislation for the change already before parliament. A separate bill from Liberal Democrat David Leyonhjelm was due to be debated in March but he decided not to go ahead without coalition MPs having a conscience vote.
Under Liberal Party rules, backbenchers can vote freely but ministers must resign if they wish to cross the floor.
Labor's policy is to allow conscience votes on the issue but deputy leader Tanya Plibersek wants the party's national conference in July to bind MPs to vote in favour of gay marriage.
Opposition Leader Bill Shorten voiced his support for Ireland's move on Twitter on Saturday.
"Time for Australia and our Parliament to embrace marriage equality. Congratulations Ireland," he said.
Mr Shorten later told reporters in Ballarat he also believed the matter was one for parliament to resolve.
He reiterated calls for Mr Abbott to allow a free vote among all coalition MPs.
Greens deputy leader Scott Ludlam hopes the Irish result moves the issue along in Australia.
"There were reports last week that we may be four votes short in the House of Representatives and we might be able to carry a majority in the Senate," he told Sky News.
His minor party colleague Sarah Hanson-Young, who proposed the bill before parliament, says she'll push for a vote on it by the end of 2015.
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