The decision by the IRA to withdraw its offer to the International Commission on Decommissioning is "very disappointing", the Minister for Foreign Affairs, Mr Cowen, has said.
The IRA's original commitment last week to the body headed by Gen John de Chastelain had been "an important contribution", he said.
"It is, therefore, particularly regrettable that they have taken today's step and I strongly urge them to reverse their decision. All of us who want to see the agreement implemented in full have worked very hard to establish a basis on which it can be achieved.
"In our proposals to the parties, the governments mapped out a way forward on four issues - policing, demilitarisation, the institutions and decommissioning.
"It is the settled democratic will of the people of Ireland, North and South, that the Good Friday agreement be comprehensively and fully implemented. There is an obligation on everyone involved in this process to see that that is achieved in the coming weeks," he said.
The Labour Party's deputy leader, Mr Brendan Howlin, said the IRA's move was "very disappointing".
He urged the organisation to reconsider its decision and to resume immediate contact with Gen de Chastelain's decommissioning body.
"This announcement is an untimely setback to the process given the significant step forward taken by the IRA last week. This development comes amid hopes that the suspension would provide the space necessary to advance discussion on the outstanding issues of decommissioning and policing," he said.
The statement would "undoubtedly cast a shadow" over talks due to be held over the next six weeks, he said: "But it must not be allowed to derail the entire process. There should be no engagement in the blame game but rather a focusing of minds on a fresh series of negotiations.
"The price of the peace process failing is too horrific to contemplate. All sides must ensure that the Good Friday agreement is implemented in full," Mr Howlin said.
The IRA's change of heart is a deep blow to the Government, which last week emphasised the historical significance of the organisation's commitment to decommission weapons.
The language used in yesterday's IRA statements has caused concern in some quarters.
For instance, the statement refers early on to the existence of an agreement between the IRA and the International Commission on Decommissioning.
However, the statement later refers to this as "a proposal". It cannot have been both, said one Government source last night. The Government welcomed the fact that the IRA has not cut off contact with the IICD.
Furthermore, Government sources said Ulster Unionists did not reject last week's statement from the International Commission on Decommissioning, as the IRA had alleged.
The British government is expected to publish plans to reform policing in Northern Ireland in a few days' time. If acceptable to republicans, this occasion might allow the IRA to make a conciliatory statement, said one Dublin source.
