Fine Gael has called for a conference of all the parties that negotiated the Belfast Agreement to take place this week.
In a joint statement, the party leader, Mr John Bruton, and the Northern Ireland spokesman, Mr Brian Hayes, said it was time for the real causes of the crisis to be removed.
"Verbal formulae or procedural devices will not suffice unless the substance of the problems is overcome," they said.
They agreed with the Sinn Fein call for an emergency Executive meeting and said Mr David Trimble had created a crisis around Friday's North-South Ministerial Council meeting with far too little time to resolve it. They were also highly critical of the paramilitaries' failure to begin decommissioning. They said Mr Trimble's call on the IRA to engage with the de Chastelain commission was "not an awful lot to ask . . . Not a single weapon has yet been decommissioned by any paramilitary," they said.
Decommissioning, they said, was not a sectarian issue, as the majority of people on both sides of the Border had voted for it in the referendums. "The majority, of course, also want police reform, but they want the two to go hand in hand, not one before the other, as suggested by the IRA."
The party rejected the argument that decommissioning was not a crucial issue so long as the weapons were not in use. "The very existence of such arms dumps is an unspoken threat. Republicans or loyalists insisting that their arms remain in place are in effect insisting that a right exists, in unspecified circumstances, to use them."
There was a collective failure of nationalism "to get the IRA to live up to the terms of the Belfast Agreement on decommissioning". That failure should be honestly analysed, the statement said, as it had helped put Mr Trimble "in the weak position he was in last Saturday".
Those who insisted on "the implementation of the Patten report to the letter . . . should be the first to understand why the letter of the agreement on decommissioning is important to others".
Inspections of paramilitary arms dumps could not become a feature of politics, as such international inspections "confer a form of legitimacy on the existence of the arms dumps themselves. That is unacceptable."
The statement maintained there was a developing process of legitimising paramilitaries. This included not treating punishment shootings as a breach of the ceasefires as well as "the reverential way in which IRA statements are treated in the media as holy writ, around which mere elected politicians must make compromises".
They said they agreed with the "reasonable point" made by Mr Gerry Adams that "Sinn Fein does not hold Executive position by dint of patronage from the UUP". But everyone in the Executive held their position by dint of patronage from everyone else.
"David Trimble and the unionist members hold their position at the discretion of Sinn Fein and the SDLP, and vice versa. If the majority in either community withdraws, the whole structure comes down. That is the way the deal was put together," the statement said.
"That structure obliges unionists to go out of their way to meet nationalist sensitivities, but it also requires nationalists to do the same for unionists. We have the feeling that the grassroots on both sides do not understand that and that their leaders are not telling them.
"The best way to get leaders to lead," the statement said, "is to get them all around the same table. That should happen this week."