The IRA statement has been described as "too little, too late" by dissident Ulster Unionist MP Mr Jeffrey Donaldson.
It was, however, welcomed by the SDLP leader, Mr John Hume, who described it as a "positive development". He appealed to all parties to exercise common sense to salvage the North's institutions.
A spokesman for the UUP leader, Mr David Trimble, said: "Mr Trimble will not comment until the morning when he has actually seen the statement."
Sinn Fein's Mr Martin McGuinness, the Education Minister, also refused to comment "until I have seen the statement for myself".
Mr Donaldson said nobody could be satisfied with the statement which went not nearly far enough. "The IRA statement only marks time and confirms that the IRA have proposed a scheme for the decommissioning of weapons to the Independent International Commission on Decommissioning. It does not specify how they intend to do it nor when.
"Our position remains that in the absence of any actual decommissioning the power-sharing Executive cannot continue in its present form with Sinn Fein ministers in position of government.
"The lack of content of this statement is only matched by the IRA's lack of action. Too little, too late," he said.
His views were echoed by another Ulster Unionist MLA critical of the Belfast Agreement, Mr Danny Kennedy. He said the statement was a "huge disappointment".
"This falls far short of what the whole process required, namely an actual act of decommissioning by both loyalist and republican paramilitaries. It is a major let-down that after over three years the republican movement still fails to honour its obligations under the Belfast Agreement.
"It is a huge disappointment and the political institutions will suffer as a consequence. Everybody will now understand the Ulster Unionist position and identify with it. It is a highly cynical statement and shows that republicans have used the entire process to wring out concession after concession while the ordinary decent people of Northern Ireland have suffered all the pain."
Mr Hume, however, said it was important that people start to trust Gen John de Chastelain and his commission. "This statement makes it quite clear that a method has been agreed by the IRA and the IICD, who are a panel of international experts. As such it is a welcome and positive development.
"People must not forget that the IICD are independent international experts in this field who deserve our trust.
"I hope this positive development will ensure that common sense will govern our approach to the current situation and that our institutions will stay in place."
The DUP's Mr Ian Paisley jnr was scathing about the statement. "This is a non-statement about a non-event. It is quite clear that the IRA are snubbing their noses at everyone and that this process is simply about them and their ego."