The decommissioning of weapons was an essential part of the Belfast Agreement, the Taoiseach said.
"The institutional and constitutional aspects of the agreement are at its core," Mr Ahern added, "but, as I said earlier, all elements must be implemented. In particular, although decommissioning is a voluntary act and cannot be imposed, it is essential, as all parties have recognised."
The Government's consistent position had been that it wanted to see the earliest possible decommissioning. The role of Gen de Chastelain and his commission would be central in taking the decommissioning process forward, he said.
"The commission will be meeting the authorised representatives of the paramilitary organisations after their appointment and will report very shortly afterwards. Let us now be prepared to wait and see what the commission then says about the detailed issues involved and not involve ourselves in speculation."
Mr Ahern said the Government was planning for, and expected, success. "If there is difficulty, either in relation to devolution or decommissioning, we are by definition in a very serious situation.
"In those circumstances, where the agreement was in significant respects not being implemented, the governments would have to step in and assume their responsibilities, including through appropriate suspension arrangements. But, let me repeat again, we are not planning for failure."
Despite the massive public support for the agreement, as expressed in the referendums, and despite the appalling outrage that was the Omagh bombing, a handful of dissidents continued to threaten the peace, the Taoiseach said.
"The Government will take further vigorous pre-emptive action to frustrate the activities of any dissidents who do so. We will at the same time continue to refute a deeply flawed and outdated political analysis which misleads people into attempting futile but potentially lethal attacks that risk killing innocent people, whether in Northern Ireland or elsewhere.
"We have the laws in place to deprive them not only of their liberty but of their property, and those laws will be used to the full in the case of any dissident group or individuals who store arms for use or otherwise attempt to destabilise the peace. "The British authorities will, I am certain, continue to move with equal determination against dissidents on all sides there, including those responsible for continuing sectarian attacks."
Mr Ahern said that in all his dealings on the issue over the past 19 months, decommissioning was part of the agreement. "Decommissioning happening by May 2000 was part of it. As I have said, I would like to see it happening as soon as possible. It was always a case that it was a voluntary act, but it had to happen to secure confidence in the agreement. That, strongly, is my position." He said recent statements by Mr Gerry Adams, the IRA and Sinn Fein could only be interpreted that way.
Mr Ahern was speaking during Taoiseach's Question Time.
The Fine Gael leader, Mr John Bruton, welcomed the Taoiseach's remarks. "One would hope that not only would Mr Trimble have, as the Taoiseach said, the best of luck in getting agreement, but that he needs every support from every quarter to ensure that the Ulster Unionist Council does take the right decision and works towards the full implementation of the agreement."
Mr Bruton said the new wording of Articles 2 and 3 would stand, once made. This was welcome, and should be noted by members of the Ulster Unionist Council.
He said it was greatly significant that the Taoiseach had said he believed there would be decommissioning. "For a Taoiseach to make such a statement, with all the information available to him by nature of his office, is something of great importance. That should also be seen as something of great reassurance to the members of the Ulster Unionist Council in coming to their very important decision, which is of great importance to them, for unionism and for all who live on this island and the neighbouring island."
Mr Ahern said that if there were those, and there were, who believed that, in some way, they had a greater right than the democratic political system, and could continue to engage in military activity, the Government had an obligation to take the right away. "As far as I am concerned, I can say to the House - and I know that the House supports it - the legislation we reluctantly passed in the autumn of last year will be retained as long as it is necessary. We know that it is because we found people in bunkers training, we found people moving arms, we found people still importing explosives and up to other activities.
"If those people do not desist, and it becomes evident that they are going to continue, then the full rigours of that legislation will be implemented in its toughest form."
Welcoming the Taoiseach's statement, the Labour leader, Mr Ruairi Quinn, said he could assure him of Labour's full support for "whatever distasteful but nevertheless rigorous measures which may be necessary".
Mr Caoimhghin O Caolain (SF, Cavan-Monaghan) welcomed "the positive developments in the peace process, including the reiteration by Sinn Fein and the Ulster Unionist Party of their commitment to implement all aspects of the Good Friday agreement and the statement by the IRA that the agreement will contribute to a lasting peace."
He repeated his request to Mr Ahern to raise with the British Prime Minister the need for urgent progress on demilitarisation, particularly in south Armagh.
"Is it not hugely unhelpful, at times such as this, that the Minister for Foreign Affairs has indicated in a reply to me recently that he has no intention of visiting south Armagh, as he promised to do over a year ago?"
Mr O Caolain asked if the Taoiseach had raised with the British Prime Minister the recent discovery in Stoneyford Orange Hall, Co Antrim, of so-called confidential British army files on 400 nationalists in different parts of the North.
Mr Ahern said the files issue was of deep concern to the Government and it was following it up. He added that he had met many groups in south Armagh wishing to meet him. Mr Joe Higgins (Socialist Party, Dublin West) said it was the desire of a huge majority of ordinary people in the North for peace that encouraged the parties to turn away from the disastrous sectarian and paramilitary strategies employed over the past 30 years.