Sinn Féin and the SDLP insisted the review was centred on the operation of the Belfast Agreement and was not a renegotiation of the deal.
Mr Gerry Adams, the Sinn Féin president, criticised the Northern Secretary, Mr Murphy, over the suspension of the Stormont institutions which has been in place since October 2002.
"The British government had no right to suspend the institutions, and had to step outside the agreement to unilaterally take that power on themselves and I do not accept for one second the British secretary of state's defence of this action," he said.
He added that nearly three months after the Assembly elections which saw a majority vote for pro-agreement candidates, crisis remained.
He accused the British government of inconsistency for insisting that the agreement was the only template for a settlement while refusing to restore the Stormont institutions. These were the "democratic core" of the agreement, he said.
He also challenged the DUP to explain how it proposed to contribute to a review on implementation of the agreement while vowing to bring it down.
Mr Mark Durkan told the two governments and the other parties that the agreement remained the best and only way forward.
"No one party's mandate at the last election can set aside or override the agreement's mandate in the referendum from the Irish people at large, including a large majority in the North. Nor can one party's anti-agreement mandate supersede the pro-agreement mandate of the other parties elected," he said.
He blamed the political impasse on the failure of paramilitaries to end their activity and on the reluctance of unionists "to uphold the inclusive political institutions".
The Ulster Unionist leader, Mr David Trimble, claimed the review was "long overdue". Yet he added that it would not address what he called the "underlying problem of Northern Ireland's political institutions" - indeed it could well help to mask it.
This problem, he said, was "the failure of republicans to decommission all their weapons and to end all paramilitary activity". He forecast: "Until that happens there is no prospect of real progress in these discussions."
He reiterated his call for "an immediate and total end of all forms of paramilitary activity".
The Democratic Unionists are vowing to take the review seriously and are promising to make known their proposals on the future of devolution in Northern Ireland to the British Prime Minister, Mr Blair.
The party is to meet Mr Blair in London tomorrow and to publish their proposals at a press conference in Belfast on Friday morning.
The Rev Ian Paisley said he shared the review table with Sinn Féin in the same way that he shared the Assembly with their representatives before suspension. He said he had not negotiated with them and would not do so.