Senator Sarah Hanson-Young has a private member’s bill before parliament and the party will move to hold the debate on 18 June

The Greens have brought forward a Senate debate on their marriage equality bill in a bid to capitalise on momentum for change following Ireland’s successful referendum to introduce same-sex marriage at the weekend.

The Greens senator Sarah Hanson-Young has a private member’s bill before parliament on changing the Marriage Act to remove restrictions on marriage being between a man and a woman.

The party will move to have the debate on the bill brought forward to 18 June, with a final vote slated for 12 November before parliament rises for its summer break.

“Gay and lesbian Australians deserve better than being treated as second-class citizens. It’s well and truly time the parliament acted,” Hanson-Young said. “The time is ripe for marriage equality in Australia. There’s more MPs in support of marriage equality now than there’s ever been and it’s time we got on with ending discrimination.”

But any change to the Marriage Act can happen only with the support of the Coalition. Tony Abbott has refused to concede ground on granting a conscience vote, saying it was up to the party room to decide.

“It came before the commonwealth parliament in the last term. It was dealt with fairly decisively then,” Abbott said of a vote on same-sex marriage that was defeated in 2012.

“It’s up to members of parliament who are eager for change to decide whether they want to bring it forward. If there is a strong desire to bring it forward then, obviously, it would be dealt with in our party room just as I imagine it would be dealt with in the Labor caucus and appropriate decisions would be made and votes would or wouldn’t go forward on the basis of those decisions.”

The communications minister, Malcolm Turnbull, on Monday night said Australia was “the odd one out” among Commonwealth countries that have passed gay marriage laws.

On Tuesday Turnbull said the proposed changes had a good chance of passing into law if the Coalition granted a conscience vote.

“I’m confident the matter will be dealt with in the course of this year and of course, we obviously need a bill. There is a change in sentiment all the time,” he said. “I have never seen a social issue which has changed attitudes as rapidly as this one. So my feeling is that it is very likely to pass,” he said.

But other members of the frontbench were more forthright.

“The voters of Groom are still opposed to same-sex marriage,” the industry minister, Ian Macfarlane, told ABC Radio. “This is not a frontline issue for me. I’m not going to be distracted by it.”

“It’s what the party room decides in the end,” he said. “I’m quite open to that discussion.”

A number of Labor MPs, most recently the manager of opposition business, Tony Burke, have abandoned their opposition to gay marriage, saying the party must move with public sentiment.

The deputy Labor leader, Tanya Plibersek, has proposed that Labor ditch its policy of allowing conscience votes on the issue, instead pushing for a binding vote that supports same-sex marriage. The proposal will be voted on during Labor’s national conference later in the year.

Plibersek and the Liberal Democrat senator, David Leyonhjelm, also have bills before parliament supporting gay marriage. The debate for Leyonhjelm’s, slated for March, was postponed due to a lack of support from the government.