Sinn Féin has said elements within unionism and "the British system" want to demolish the peace process, rather than build upon it.
The party chairman, Mr Mitchel McLaughlin, said at an ardchomhairle meeting in Julianstown, Co Meath that the IRA statement had presented a significant opportunity which was not being grasped.
Mr Gerry Adams and Mr Martin McGuinness did not attend, remaining instead in the North as intense behind-the-scenes negotiations continued to reach a deal.
"Regrettably, in my view there are those within unionism and within the British system who are still locked into the old agenda, who want to demolish the peace process, not build it," Mr McLaughlin said.
"One of the difficulties is that the unionists have left their negotiation to the British government. There is no clarity or certainty around UUP intentions."
Neither was there "certainty of completion" in the two governments' joint declaration, he said. "It is full of conditionality within a protracted process. The IRA statement is clear and unambiguous. Even the British government has acknowledged it shows the desire of the IRA to make the peace process work," Mr McLaughlin said.
"That is an unprecedented development. It should be built upon. The two governments should publish their joint declaration. The British government should lift the suspension of the institutions and move to the election of a new assembly."
Mr McLaughlin said the governments' joint declaration should ensure that the "rights and entitlements", still not achieved five years into the Belfast Agreement, became a reality.
Meanwhile, a Sinn Féin Assembly member, Mr Gerry Kelly, claimed the Ulster Unionist Party was more interested in dictating events than in moving the process forward.
He was responding to comments by the UUP leader, Mr David Trimble, that the IRA statement fell "a long way" short of what was needed to restore the North's Executive and Assembly.
"I am not going to go into detail," said Mr Trimble. "That detail will, no doubt, become apparent, and when it does you will see just how far short this is."
Mr Kelly replied: "David Trimble's focus is on dictating terms rather than on making this process work. Unionists cannot be allowed to frustrate the peace process.
"Too often in the past the British government has allowed unionism to determine the pace of change. The rights and entitlements of nationalists and republicans cannot be dictated by unionists. The politics of veto cannot be allowed to stop progress."
The anti-agreement UUP MP, Mr Jeffrey Donaldson, said the Assembly elections must proceed on May 29th next in preparation for a power-sharing administration without Sinn Féin.