An Ulster Unionist MLA does not believe any of his nine Assembly colleagues would sign a petition of concern to block same-sex marriage.
Speaking at the annual Pride Talks Back Debate in Belfast, Doug Beattie apologised to the LGBTQ community for his party's failure to support gay rights for so long.
He acknowledged it had "missed the bus", but stressed that it was now doing everything possible to "catch up" and "reach out".
The DUP was the only one of Northern Ireland's five main parties who didn't send a speaker to the event in The Mac on Monday night. The party said no one had been available.
The DUP's absence will be seen by some as a step backwards from Arlene Foster's presence at a PinkNews reception in Stormont last month.
A question-and-answer format in front of an LGBTQ audience would be more challenging for a DUP speaker. However, East Belfast MP Gavin Robinson attended the 2012 Pride Talks Back when Lord Mayor of Belfast.
Sinn Fein president Mary Lou McDonald, SDLP MLA Claire Hanna, Alliance MLA John Blair and PUP councillor Billy Hutchinson attended Monday's event.
Mr Beattie said he was working hard to convince people that "unionist does not mean anti-LBGTQ, because it doesn't".
A majority in the Assembly supports same-sex marriage but a petition of concern with 30 signatures could block a change in the law. The DUP has 28 MLAs, and TUV leader Jim Allister has said he would support his former party on this issue. There has been speculation that UUP East Antrim MLA Roy Beggs may also sign.
Mr Beattie said same-sex marriage was a conscience issue for his party and he fully supported a change in the law.
"The reality is I have one vote and that one vote counts, and Roy Beggs has one vote and that vote counts," he said.
"The other eight MLAs have one vote and that one vote counts, and anyone who signs a petition of concern negates my vote." Mr Beattie said it was his personal view that none of his party's MLAs would sign a petition of concern to block equal marriage.
"Roy is a really decent man, he is a democrat. Do I think he will sign a petition of concern? No, I do not," he said.
"That's not to say he won't, but I'm saying the person I know will not sign a petition of concern and neither would anybody else of the MLAs in the Ulster Unionist Party - but we will vote with our conscience."
Apologising for the UUP's past failure to support equality for gay men and women, Mr Beattie said: "I am on a journey. My party is on a journey, but here's the problem. The journey has started and I missed the bus. My party missed the bus.
"We are behind where you are now so we are in the position of having to learn, of having to catch up, of having to reach out."
Mr Beattie said that a 2015 speech by former UUP leader Mike Nesbitt, in which he warned that those who oppose same-sex marriage were on the wrong side of history, was the first step of the party's journey.
Mr Nesbitt established a working party to address LGBTQ issues which the Upper Bann MLA heads.
"He has sent me off to talk to people, to find out the problems, to engage - not just for a box-ticking session but a meaningful engagement," Mr Beattie said.
UUP representatives now attend training sessions run by the Rainbow Project and Cara Friend. "We need it," he added.
Mr Beattie said that Mr Beggs was among the MLAs at the sessions. "He wants to move this forward, the same as everybody else," he said.