The Sinn Fein president, Mr Gerry Adams, has said the IRA's withdrawal of its proposal to put weapons beyond use is not surprising.
The British government's brief suspension of the Assembly and the Ulster Unionists' failure to welcome the statement from the Independent International Commission on Decommissioning were not constructive, he said.
The SDLP leader, Mr John Hume, described the IRA move as "strange and unhelpful" and said it played into the hands of anti-agreement unionists.
The arms issue would be resolved only in the context of further progress on policing and demilitarisation, he said. "I believe the IRA proposal was a very genuine one but, more important than that, it was endorsed by the Independent International Commission on Decommissioning.
"For the unionists to reject the IICD's determination and for the government to do what it did is hardly the stuff of peacemaking," he said.
"That is the clear duty of all parties, given the awful alternative of returning to the past. This statement makes that task all the more difficult and, as such, I call on the IRA to immediately withdraw it."
The Sinn Fein chairman, Mr Mitchel McLaughlin, also blamed the crisis on the UUP and the British government.
"The willingness of the British government to unilaterally suspend the institutions is in marked contrast to their refusal to use their powers to ensure Sinn Fein ministers could attend the All-Ireland Ministerial Council.
"The clear intention of the unionists, as spelt out by David Trimble last October, is to create a crisis, blame republicans, achieve suspension and renegotiate the agreement," he said.
"The present crisis is the result of the British government's failure to implement the Good Friday agreement. This failure has created the space from which the unionists are attempting to subvert the agreement. The onus is now clearly on the British government to live up to its responsibilities," Mr McLaughlin said.
His party remained committed to the Belfast Agreement and to working with both governments to ensure its implementation.
When asked to comment on the arrests of three Irishmen in Colombia, he said: "People should be patient. Information is scant. People have been arrested but nobody has been charged. Nobody has signed confessions. I think all of us are experienced enough to know there is a propaganda dimension the way this information has been filtered out."
The Sinn Fein chairman confirmed that some of the men detained in Colombia were known republicans, but he insisted there was no basis for concluding the arrests had any bearing on the peace process.
"The issue is whether this has anything to do with the Irish peace process. I think there is no basis for coming to that conclusion."