The Greens have moved to push federal parliament to a vote on same-sex marriage before the end of the year.

Renewed debate in Australia has been triggered by Ireland's vote in favour of marriage equality in a referendum on the weekend.

Same-sex marriage has already been legalised in several countries, including the United Kingdom, Canada and New Zealand.

Greens senator Sarah Hanson-Young said her party's Marriage Equality Bill would be brought on for debate in the Senate on June 18, with a view to vote on November 12.

Senator Hanson-Young said it was time Australia "really caught up".

"This gives members of all parties the opportunity to think about how they will vote on this issue but also the impetus for Tony Abbott to allow his party room to have a free vote, to vote with their hearts as well as their heads," she said.

Prime Minister Tony Abbott, who remains opposed to same-sex marriage, has said it is up to the Coalition party room to decide if the issue warranted a conscience vote.

The issue was not brought up at this morning's joint party room meeting, but yesterday Liberal supporters of marriage equality said the discussion was "close".

Labor has granted MPs a conscience vote on marriage equality, however deputy leader Tanya Plibersek is pushing for a binding vote in favour of the issue.

Opposition Leader Bill Shorten has baulked at that, setting it up as a flashpoint for the party's July national conference.

A growing number of ALP MPs are switching their vote to support the idea, with frontbencher Joel Fitzgibbon the latest to add his voice to a yes vote, citing a change in popular sentiment.