Suspension of the Executive and Assembly provided an opportunity for the parties to come up with an agreement which enjoyed majority support among nationalists and unionists, the DUP said yesterday.
The Rev Ian Paisley said: "What we need to do now is get back to the drawing board and face up to the issues that brought this thing to an end. No government can force its will upon the majority of the electorate," he said.
The party leader demanded new elections and accused the British government of trying to force upon unionists a form of government that was unacceptable to them.
He insisted: "We will not be negotiating with IRA-Sinn Féin. Full stop. Period."
The SDLP leader, Mr Mark Durkan, regretted the suspension but welcomed the commitment of the two governments to continue implementing other aspects of the Belfast Agreement. He also claimed that the task ahead should be centred on the causes of the lack of trust and confidence which led to suspension. He said there should not be a cooling-off period.
He wished to "clear up some misleading reports" that he was being pressed by the Irish Government in relation to proposals for shadow roles or consultative functions for himself and Mr David Trimble.
"That proposition formed no part of any discussion I had with either the Prime Minister or the Taoiseach last week. No part whatsoever."
He added he didn't want to get involved in the "furniture arrangement" of direct rule and claimed that SDLP faith and confidence in the agreement had not dissipated.
He insisted faith and confidence could be rebuilt among the parties and that the public, including the unionist public. could be given "a full working version of the agreement, and people will see that this time it isn't a breakdown waiting to happen".
For the Ulster Unionists, Sir Reg Empey claimed that ministers were "being ejected from office ... because the government has failed to honour its obligations to deal with people who are deemed to be committed to exclusively peaceful means".
He denied Sinn Féin claims that unionists were opposed to change, could not accept power-sharing with Catholics and were soft on loyalist paramilitary violence.
Sir Reg pointed to what he saw as a change in tactics by the DUP. He said there was "a courtship dance between the DUP and Sinn Féin".
The IRA could not escape the reality of paramilitary activity, he said.
"Did I imagine what happened over the weekend in Co Wicklow? Have we all imagined beatings in Londonderry and south Armagh? Did we all imagine the discovery of a spy ring? Did we imagine Colombia, did we imagine Florida? I think not."
He said republicans had "dirtied themselves" by that sort of activity, and it was totally incompatible with the commitments under the Belfast Agreement.
He said the UUP sought implementation of the agreement's terms.
The Alliance leader, Mr David Ford, pressed republicans to act to restore faith in the political process. "While there are criticisms we have to make to the UUP for their failure to fully defend the agreement, this crisis has not been brought about by anything other than the behaviour of republicans," he said. "It is quite clear that republicans should have been punished, not all the other parties."
The Sinn Féin president accused the Northern Secretary of dishonesty. "You cannot talk about democracy while suspending now for the third time in his term as Secretary of State the institutions," he said.