The Sinn Fein president, Mr Gerry Adams, has described the decommissioning of paramilitary weapons as a "cul-de-sac, a dead-end issue".
"The peace process has brought us to an important juncture in the evolving relationships between the people of this island. It is a fragile process which needs to be continuously promoted and consolidated if it is to achieve a democratic peace settlement.
"The Good Friday Agreement is an important step along the road to that goal. Our immediate priority therefore must be to avoid stalemates, cul-de-sacs, brinkmanship, broken promises, or bad faith.
"The decommissioning issue is a cul-de-sac, a dead-end issue. It was thoroughly discussed and negotiated during the talks process. The conclusions to those deliberations are contained in the Good Friday Agreement.
"The Good Friday Agreement sets out a clear timetable and chronology in respect to establishing the executive, the departmental structures, a fully functional all-Ireland Ministerial Council and the Civic Forum. There must be urgent progress on this," Mr Adams said.
He said "there can be no Assembly without these interdependent and interlocking institutions", and added: "All political leaders need to keep the commitments they made. Trust can only be created by keeping promises, not renegotiating them."
An Ulster Unionist Assembly member, Dr Esmond Birnie, dismissed as "a fiction" any suggestion that the Belfast Agreement "allows an open door for Sinn Fein into the executive ahead of the beginnings of a process of disarmament".
Dr Birnie, who represents South Belfast, accused the Democratic Unionists and UK Unionists of spreading "unfounded alarm". "I refer them to the requirements inherent in the pledge of office; Mr Adams and Mr McGuinness cannot make such pledges whilst being inextricably linked to a private army."
On the position of Mr David Trimble, Dr Birnie said: "Anyone within our party who contemplates bringing down the leader must realise that in so doing they will destroy the Assembly. I do not think Northern Ireland public opinion would forgive them for that."
A UUP Assembly member for North Antrim, the Rev Robert Coulter, compared Sinn Fein to Pontius Pilate: "It is not enough for Sinn Fein/IRA to hold up Pilate hands and say - we have no weapons. If they are sincere in embracing peace, they must ensure that these weapons are destroyed."
The Ulster Unionist MP for Lagan Valley, Mr Jeffrey Donaldson, commenting on reports that Mr Trimble had threatened to resign as First Minister, said:
"He is not bluffing. He is aware of the deep unease within the party and this warning accurately reflects what he has been saying privately over the last couple of weeks."
Mr Donaldson added: "There has to be a credible start to the decommissioning process before they (Sinn Fein) can possibly qualify for ministerial office.
"Decommissioning was fudged before negotiations and during negotiations, and republicans are now trying to fudge the issue again.
"But let me make this absolutely clear - we have reached the bottom line. This is an integral part of the agreement. We have prisoners being released. We have an Assembly and now it's for the terrorists to disarm," Mr Donaldson told the Press Association.
The chairman of the Workers' Party, Mr John Lowry said he would be putting "the strong anti-sectarian, working-class case" at the Labour Party conference in Blackpool next week. Mr Lowry will be addressing a fringe meeting, along with Mr David Ervine of the Progressive Unionist Party.