Gay marriage is expected to be back on the parliamentary agenda when it resumes after the winter break, but the prime minister says his views on the matter are unchanged.
The US Supreme Court ruled on Friday that marriage equality is a nationwide right, meaning same-sex marriage is now legal across all American states.
The decision sparked calls from supporters and politicians for Australia to move on marriage equality.
But Tony Abbott says Friday's historic decision is a matter for the US, just as the referendum in Ireland was a matter for the Irish.
"Obviously there is a lot of community debate going on," Mr Abbott told reporters in Melbourne on Saturday.
"I have views on the subject which are pretty well known and they haven't changed."
However, cabinet minister Christopher Pyne says a vote could be held before the end of the year.
"There appears to be growing momentum worldwide towards marriage equality and our parliament will deal with it at the appropriate time in the appropriate way," he said.
"When we come back in spring, there's every possibility that will be back on the agenda."
Labor and the Greens have backed growing calls for marriage equality in Australia.
The US had upheld the truth of equality for all, Labor leader Bill Shorten and deputy Tanya Plibersek said in a joint statement, backing calls for action by the parliament.
"If we want the whole parliament to own it, I extend the invitation again to Mr Abbott that a Liberal can move it," Mr Shorten later told reporters.
"For us, it's not about who moves it and who seconds it. For me, it's about the outcome."
But he said in return for a Liberal moving the legislation, he urged Mr Abbott to agree to a free vote for Liberal Party members.
"That's all that people are seeking. Marriage equality should not be a party political issue," Mr Shorten said.
Former prime minister Kevin Rudd also hailed the decision and said on Twitter it was "time now for Oz to act".
The Greens said the US ruling was the loudest call yet for marriage equality in Australia.
But the renewed push for marriage equality has not met with universal support; the Australian Christian Lobby and the Australian Marriage Forum have decried the US decision.
"The US Supreme Court has ushered in a new era of civil discord with its politically activist and morally reckless ruling on homosexual 'marriage'," Australian Marriage Forum president Dr David van Gend said in a statement.
"We must not let that happen here."
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