"I hope that people will consider carefully what is involved and will respond constructively to this opportunity created by these negotiations," he said.
The IRA has said that it will allow its secured arms dumps to be inspected by international inspectors to prove that it has put its weapons beyond use and that it will re-engage with the decommissioning commission.
The statement came after the British and Irish governments announced that they hoped to restore Northern Ireland's executive on 22 May and see all areas of the Good Friday Agreement including decommissioning implemented by June 2001.
Catholic Primate of Ireland Archbishop Sean Brady said be believed the political developments had the potential to deliver lasting peace to Northern Ireland.
"I hope that people will consider carefully what is involved and will respond constructively to this opportunity created by these negotiations," he said.
"A genuine opportunity now exists for a resolution of the conflict in Northern Ireland. The prize of lasting peace has never been more closely within our reach.
"I welcome the significant progress made over recent weeks to restore the institutions of the Belfast Agreement. I pay tribute to those who have worked with such determination to do so.
"Despite the genuine difficulties still to be overcome on all sides, I believe these events provide solid grounds for new hope and fresh confidence."
President of the Methodist Church in Ireland, the Reverend Kenneth Wilson also welcomed the developments.
He called on everyone to work together to build peace and stability for the people of the province.
Unionists still considering offer
The Ulster Unionists are still considering whether the IRA's statement on arms is enough to persuade them to return to the executive.
Ulster Unionist leader David Trimble urged people to be cautious of the IRA statement.
But he said he hoped he could bring his party with him into a process of restarting Northern Ireland devolution if he could verify that the "promising" IRA statement would lead to "complete and permanent decommissioning".
The Northern Ireland peace process has been deadlocked since February following the government's decision to suspend the political institutions during the dispute between Sinn Fein and the Ulster Unionists over IRA arms.
The British and Irish Governments, the nationalist SDLP and Sinn Fein have welcomed the IRA's offer, while anti-agreement unionists rejected it.
But as the main unionist party, the Ulster Unionist Party's decision about whether they will accept the IRA's statement and the government's proposals as a basis to move forward will be crucial.