If IRA decommissioning is not secured over the summer the Ulster Unionist Council should reconvene to review the party's position on the process, according to the anti-agreement MP, Mr Jeffrey Donaldson.
Speaking after Saturday's meeting Mr Donaldson, considered a contender for the leadership, also stressed that Sinn Fein would be excluded from the Executive if no IRA decommissioning occurred.
"Sinn Fein/IRA need to get the message their bluff has been called. It's time for them to deliver. They needn't think they are going to hang around Stormont in ministerial office because we will not allow them to hold office if they don't decommission," he said.
The party was united "at the moment" around Mr David Trimble's tactic to resign as First Minister on July 1st if there was no move on IRA arms.
Mr David Burnside MP, another sceptic on the accord, firmly ruled out further concessions to nationalists on police reform.
"That game is over. Unionism has had enough. Unionism will not be making any more concessions, and if there are demands from republicanism for further concessions on policing they're going to pull this whole thing apart.
"It means this whole peace process will be jeopardised, and I think they are going to endanger peace in this community," he said. The "real crisis" in the process would come in August when the six-week period allowed for the reinstatement of the First and Deputy First Ministers had expired.
Mr Michael McGimpsey, the North's Minister of Culture, said the party was united around the leadership's current strategy.
He said if no decommissioning occurred the tactic would be to exclude Sinn Fein from government.
It would be for the SDLP to determine "how much clear blue water they want to put between themselves and Sinn Fein. At times we have felt the SDLP have been somewhat diffident in standing up for themselves," he added.
Sir Reg Empey, the Minister of Enterprise, said it was a positive meeting and the party had not "imploded" as some had predicted.
"The party decided today that it wasn't going to make a side-show of itself to get republicans off the hook on the weapons issue. We're keeping the focus on that," Sir Reg said.
He would not be drawn on speculation that Mr Trimble may nominate him as an alternate First Minister for a six-week period set out by legislation. "That's a matter for him."
Speaking to the media, Mr Trimble refused to confirm if he intended to nominate an alternate. He said he feared it would take his resignation to make republicans realise there was a crisis.