The Taoiseach ruled out the d'Hondt procedure for allocating ministries in the Northern executive being triggered this week.
"I do not believe it will be triggered this week. I have discussed the matter with the British Prime Minister. While there are no definite and final conclusions on when it might be, my view is that to trigger the d'Hondt mechanism in isolation would be a mistake," Mr Ahern said.
"We have to work out all of the procedures of what will happen between now and the end of June. Then we will have to work out: if it was triggered, could the Executive be set up? I see no benefit whatever - maybe I take a slightly different view to some people on this - of trying to set up the Executive in some shadow form for a fortnight and then standing it down. That makes no logical sense to me whatsoever. I have certainly made those views strongly known."
Mr Ahern was replying to the Fine Gael leader, Mr John Bruton, who asked if he had been consulted by the British Prime Minister and the Secretary of State as to whether the mechanism would be triggered this week and if he had expressed a view about it.
Replying to the Labour leader, Mr Ruairi Quinn, he said a failure to meet the June 30th deadline would effectively mean the agreement would be set aside.
Mr Austin Currie (FG, Dublin West) asked what the British Prime Minister meant when he said that that on July 1st, they would move the process forward or would have to look for another way forward.
Mr Ahern said it meant that the agreement as it stood would be effectively set aside. "We would have to try to find another way forward. This is what all the pro-agreement parties are now saying. However, it does not mean that certain parts of the agreement would not be taken forward in some other process."
The Taoiseach said that "any one move without thinking it all through will only lead to more grief, and we have had enough of grief".
He added that the issues were fairly straightforward at this stage. "I am clear about what requires to be done, but I am not clear whether that can be done. We are going around the houses on this issue. This will have to stop.
"It is a question of whether the people are prepared and the main parties are prepared - we all know who they are - to set up the executive and to assure each other and the governments that they mean real business. If that is possible it can be done. If it is not, we have major difficulties. We should sit down and come to those decisions."
Mr Bruton said he commended and supported the Taoiseach for the practical approach he was taking. "Will he agree that one of the reasons for the problem in regard to the decommissioning of weapons is the sense of encirclement of the nationalist community in Portadown?
"Will he agree that the Orange Order and the defenders were founded in the vicinity of Portadown and that Portadown is the centre of contention almost in north-east Ulster? Will the Taoiseach agree, therefore, that those who have the possibility of finding an agreed solution to the parades issue in Portadown have a responsibility not only in regard to that issue but for the fact that if that issue is not resolved it will make it much more difficult for many other associated issues, including decommissioning, to be resolved?"
Agreeing with Mr Bruton, the Taoiseach said there was a consensus that the "sectarian poison" being created around Portadown was having an enormously negative bearing on every other factor.
He said he had offered to send an all-party group to speak to the people on Garvaghy Road, or both sides if that would help, as an expression of sincerity from the Irish parliamentary system. "I am awaiting a response. I do not want to do that if it would be unhelpful."
Mr Ahern said the June 30th deadline was only a few days before this year's march, which would be followed by the other 1,400 to 1,500 marches. "This brings huge pressure to bear, and I will do everything possible to try to de-escalate the situation. The Prime Minister, Mr Blair, is also anxious to do so."
Mr Bruton and the Labour leader, Mr Ruairi Quinn, said they would support the Taoiseach's initiative.
Asked by Mr Quinn what would happen if the deadline was not met, the Taoiseach said he had always been committed to it. One aspect had now become apparent to him, he added, and this was that the next obvious date was the end of September because July and August were out of the question.
"However, I cannot think of anything which would change the position by delaying matters until the end of September or even December. The credibility of the agreement and confidence in it would become completely unstuck. While the last opinion poll showed steady support, that might not remain the case if matters drifted for a long period.
"In addition, the patience of the political system, and the people who are endeavouring to make the agreement work, would be tested. This includes people on all sides and even members of anti-agreement parties. I cannot speak for them because they will not meet me, but I consider that they feel there is much good in the Good Friday agreement and that it should not be delayed or deferred. The focus and determination to try to achieve as much as possible by the end of June is all around."
Earlier, Mr Bruton suggested that those who had killed Paul Downey were the enemies of the peace process. He asked Mr Ahern for his reaction to reports that the Provisional IRA were responsible for the murder and the effect it would have on the status of its ceasefire.
Mr Ahern said there had been no indication from the Secretary of State that the status of the ceasefire was under question. "There are no circumstances under which this murder can be justified, and it is to be absolutely condemned by the House."
Asked by Mr Bruton if he believed that republican elements were involved in the murder, the Taoiseach said he had no knowledge of this. "The Secretary of State is awaiting the investigation into it. The individual was known to the police."
He added that he had discussed the matter with Mr Seamus Mallon, of the SDLP, and the leader of the UUP, Mr David Trimble, and there was no certainty of what it was about.
Asked by Mr Quinn to be more explicit about his observation that the dead man was known to the police, the Taoiseach said the individual was known for some criminal activities. "I do not have any great evidence or facts about that, but I do understand from everybody I spoke to yesterday that the individual was fairly well known on the criminal side of things."
Mr Quinn said that if the IRA was retaining its arms, and was purporting to use them to effectively police parts of the island where drug-dealing was rampant, it might be left some kind of persuasive argument, however invalid, that it should retain arms.
Mr Ahern said he did not know the details of the case. Whether the dead man, or anybody else, was a drug dealer, it gave no justification whatever to any organisation to be involved in such activity in any part of the island.