Minister for Foreign Affairs Dermot Ahern today welcomed the "unprecedented clarity" of the IRA statement and said the door was now open for a deal to end the Northern Ireland impasse.
Mr Ahern said the Government was optimistic about the IRA move, but he insisted that the statement would have to be followed by action.
He said there were some concerns about the lack of a specific mention of criminality in the IRA statement, but added the Independent Monitoring Commission had been asked to submit a report on paramilitary activity next January.
The validity of the IRA's pledge to desist from violence could be properly evaluated then, he said.
The Minister said there was a desire among the Irish and British governments that the Northern Ireland institutions are restored as quickly as possible.
He was hopeful the IRA statement would create a scenario whereby the DUP could now "sit down" with Sinn Féin and work out a deal to see the two parties sharing power in the Northern Ireland Assembly.
Fine Gael also welcomed today's announcement. The party said the IRA statement "has the potential, if fully delivered on, to repair the damage done to public confidence in the Northern peace process".
"However, IRA statements on their own are no longer sufficient to convince people. The sincerity of the provisional movement will be judged by the actions it takes to implement this latest statement," the party said.
"Nothing short of the complete decommissioning of all arms and a verifiable and permanent cessation of all paramilitary and criminal activity will be acceptable.
Fine Gael called for a clarification from the IRA on the subject of criminal activity.
The Archbishop of Dublin, Dr John Neill, also welcomed the today's statement.
Dr Neill said: "The existence of private armed groups like the IRA and loyalist paramilitaries is totally incompatible with a normal, democratic free society governed by the rule of law.
"This makes today's statement a welcome development for the state and society of the Republic. Only fully accountable democratic institutions have the right and authority to act in the name of the Irish people.
"The responsibility now falls on the two Governments, society north and south and to no small extent on the Churches together to build a real peace founded on mutual understanding. I pray that God will assist us all in doing so," the Archbishop said.
Senator Edward Kennedy said the statement means we're finally nearing the end of this very long process to take guns and criminality out of politics in Northern Ireland once and for all.
I look forward to the final act of decommissioning, and the verification that paramilitary activity and criminality have ended, and the all-important restoration of the Northern Ireland Assembly."