The Ulster Unionist leader has said Sinn Féin must "get real" about the continued existence of the IRA.
Mike Nesbitt was addressing his party's annual conference on Saturday.
An assessment of paramilitary activity in Northern Ireland earlier this week indicated that the IRA still has access to weapons, although its leadership's focus is wholly political.
Mr Nesbitt said Sinn Fein's denials have "worn a hole in the fabric of devolution".
Mr Nesbitt said the UUP had given firm, decisive and unambiguous leadership in the face of the current crisis.
"We forced terrorism to the top of the talks agenda," he said.
"We left the secretary of state no choice but to commission this week's published report on paramilitary activity. A report quite shocking in its explicit analysis of paramilitary groups today. We are vindicated."
The story of Stormont's crisis
- Stormont's political upheaval was sparked by allegations that Provisional IRA members were involved in the murder of Kevin McGuigan Sr
- The row erupted after a senior Sinn Féin member was arrested as part of the inquiry into Mr McGuigan Sr's death. He was later released without charge.
- Northern Ireland First Minister Peter Robinson stepped aside and all but one of his DUP ministers resigned
- Finance Minister Arlene Foster is now acting first minister
- Read more: How Stormont's crisis unfolded
Mr Nesbitt said the current talks represent a unique opportunity for a collective political will to be expressed to rid Northern Ireland, and the island of Ireland, of paramilitarism and the associated criminality, once and for all.
"But we will not be standing shoulder to shoulder against paramilitarism with a political party that insists the IRA no longer exists," he said.
"It looks like the DUP will. What a pity they won't stand strong with us. But we will not be deflected. It's not the first time we have had to do the difficult thing on our own."
He added: "Sinn Féin will defend the indefensible by saying the IRA are butterflies who have flown away. I make this offer to them. Get real.
"We want to respect your political mandate. Make it possible for us. Get on the same page as the rest of the world - or accept the consequences of the stance you have chosen to adopt."
Mr Nesbitt said seldom does a week go by "without another astonishing revelation of the utter dysfunction at the heart of our government".
He told delegates it was the best of times and the worst of times.
"The best of times for the Ulster Unionist Party - unfortunately, it's the worst of times for the devolution we fought so hard for," he said.
Mr Nesbitt also signalled a willingness to reach out to nationalists.
"I do not have to 'hold my nose' to work with nationalists. I do not endorse the idea of 'rogue' and 'renegade' nationalist ministers," he said.
He also told those in his party who oppose same sex marriage that he believes they will find themselves on the wrong side of history
'Definition of ambiguity'
Sinn Féin's Conor Murphy said Mr Nesbitt had to "end the charades and stunts".
"Far from taking a principled and unambiguous stand, Mike Nesbitt is the very definition of ambiguity, having walked his party out of government and straight into talks with Sinn Féin," he said.
"In short, it looks like he's making it up as he goes along."
Speaking earlier, former UUP leader Sir Reg Empey said that after the report on paramilitary activity stated that PIRA members believe that the provisional army council exists and oversees both PIRA and Sinn Féin with an overarching strategy "[First Minister] Peter [Robinson] goes back to business as usual sending the clear signal to Sinn Féin that they can get away with it again. How awful".
He also said Sinn Féin's denials about the IRA were "sapping credibility out of politics and must be reversed if we are to create effective and acceptable devolution at Stormont".
Sir Reg added: "It is true that Stormont has taken some good decisions, but conference, the present administration is the worst so far and is failing on nearly all fronts. This cannot be as good as it gets."