The British and Irish governments expect IRA decommissioning will be completed quickly, following yesterday's declaration by the organisation that it is abandoning its 35-year armed campaign.
There are strong indications that the destruction of arms may be complete within weeks, while the first of a series of decommissioning acts could be several days away.
The IRA's weapons store has been centralised at a number of munitions dumps in the Republic in recent times, Government sources said last night. While the destruction of arms has not yet begun, the Government is hopeful that the entire arsenal will be destroyed before the end of August.
Putting pressure on the IRA to act swiftly following its statement, the Taoiseach said: "I'd like to see it happening sooner rather than later, because it will help the overall process of trying to move on to the next stage and get the institutions and other matters under the Good Friday Agreement up and running."
The IRA's statement was greeted with cautious optimism by Mr Ahern and British prime minister Tony Blair. Mr Blair said it would be "momentous and historic" if "borne out by actions".
The statement was greeted by the White House as "important and potentially historic". White House spokesman Scott McClellan said republicans must now demonstrate "their unequivocal commitment to the rule of law".
In yesterday's statement, ordering an end to its armed campaign, the IRA "compelled" all members to dump arms, operate by purely peaceful and democratic means and not "engage in any other activities whatsoever".
"All Óglaigh are compelled to fully comply with these orders," the statement said.
Two still unchosen clergymen, one Protestant, one Catholic, would witness the destruction of the IRA's arsenal, along with Gen John De Chastelain of the International Independent Commission on Decommissioning.
Independent Monitoring Commission reports due in October and next January will help the governments decide if all IRA paramilitary and criminal actions have ended, the Taoiseach and Mr Blair said.
Unionists reacted cautiously to the IRA statement. The DUP leader the Rev Ian Paisley said: "We will judge the IRA's bona fides over the next months and years based on its behaviour and activity."
Northern Secretary Peter Hain told The Irish Times the statement would be followed by talks on the devolution of policing and reducing troop numbers. A truth and reconciliation commission and the removal of watchtowers and checkpoints would also be discussed.
Mr Hain added: "This is not 1969. This is a post 9/11 world of suicide bombers in London. We cannot have terror in the current climate."
Talks between Sinn Féin and the Democratic Unionist Party about reforming the Northern Ireland Assembly and Executive are unlikely before the New Year, Minister for Foreign Affairs Dermot Ahern said. The Government had not demanded that decommissioning be photographed in talks with Sinn Féin, he added. "This is a unilateral decision by the IRA to disarm. Photographs were not on the table and were never proposed in any of the discussion," he said.
The Taoiseach was confident that the IRA statement covered criminality as well as paramilitary actions, though he added: "People are right to be sceptical because we have seen so many false dawns."
In Dublin, Sinn Féin leader Gerry Adams said IRA members and Republicans must "stay united".
"Some people may never come to terms with it. Maybe it is a step too far for some Republicans," he said.