Bill Shorten will move his own private member’s bill on marriage equality, seeking to use the momentum from Ireland’s historic vote in favour of same-sex marriage to force the Australian parliament to reconsider the issue.

The opposition leader has given notice that he will move his private member’s bill on Monday, seconded by his deputy Tanya Plibersek, who had herself foreshadowed a private member’s bill in 2014.

Labor has rejected Plibersek’s push for a binding yes vote on the issue, with Shorten saying Labor MPs and senators would vote according to their conscience. He said that for marriage equality to succeed, the prime minister had to also allow Coalition MPs and senators a conscience vote.

Shorten said he understood his bill “will not have the universal support of my colleagues” and would “challenge the deeply held personal beliefs of MPs and senators on both sides of politics”.

Abbott said on Sunday that the issue had been “dealt with fairly decisively” when it was defeated in 2012, but repeated that it would be up to the Coalition party room to decide whether to abandon the current position against marriage equality in favour of a conscience vote.

“If it comes before our parliament again, our party room will deal with it, our party room will decide whether our existing policy continues or not and then we will have a good debate,” he said.

“But, can I just say this: not for a second – not for a second – do I want to underestimate the feelings that people have on this issue, both for and against. Not for a second.

“Good people can be on either side of this question. Decent people can disagree on this issue. There are a range of views inside the parliament. There are a range of views inside my party room. Frankly, there’s a range of views inside my family – inside the Abbott family – I am probably the last hold-out for the traditional position.”

Shorten’s move – which comes as Greens senator Sarah Hanson Young brought forward Senate debate on her marriage equality private member’s bill – will increase pressure on the Coalition to have a party room discussion on the issue of a conscience vote.

The communications minister, Malcolm Turnbull, said he thought marriage equality would be voted on this year, and would pass if the coalition allowed 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.”

Shorten said he believed “the time has well and truly come for the parliament to debate marriage equality”.

“Our current law excludes some individuals ... it says to them, your relationships are not equally valued by the state, your love is less equal under the law.”

“The world isn’t waiting for Tony Abbott and our parliament shouldn’t have to,” he said.