The Taoiseach said the so-called `Real IRA' could not hope to take on the people of Ireland and win. "They have already disgraced themselves and the name which they have misappropriated," Mr Ahern said. "There is no community in Ireland that wishes to have them operating in their midst.
"The INLA acknowledged in their ceasefire statement, which I welcome, that the new conditions created by the (Belfast) agreement demand a ceasefire, and that the onus on all is to ensure that the democratic wishes of the Irish people are upheld."
Mr Ahern said the House expected and demanded that all remaining groups would follow suit, or they could face the consequences. "These people are about to learn a lesson that will teach them to respect the strength of Irish democracy. The time for sophistry that provides a cover for murderous attacks on fellow Irish men and women is over."
He added that those who organised and carried out the horrific act of violence in Omagh had a stark choice. "They can heed the will of the Irish people now and tell us - and convince us - that their violence is at an end for good. Or they can defy us to put them out of business.
"If they do, they should not be in any doubt about this Government's determination to crush and dismantle any organisations that still engage in violence, as I made clear prior to the Omagh bombing.
"They should be in no doubt about our determination to do everything we can to assist in bringing the perpetrators of this terrible crime to justice. We are determined that the people of this island, North and South, will enjoy the peace that they democratically endorsed, and we are determined that the victims of Omagh will have justice."
The Taoiseach said the Government had decided on a security and legislative response to the challenge of the Omagh atrocity which was extremely tough, even draconian, but that would stay in force only so long as it was required. He was satisfied, however, that the response reflected and expressed the will of the vast majority of the people on the island.
"In all normal circumstances, we would not now be asking the House to enact new legislation, which we are doing only with the utmost reluctance, out of the necessity of protecting all the people of this land from any other Omaghs."
Mr Ahern said that neither he nor the Garda had ever underestimated the potential threat posed by the new organisation since last December. Every effort had been made through a tough security counter-strategy to dissuade them from continuing and to frustrate their operations, insofar as the Government could from the Republic's side of the Border.
The Garda had achieved considerable success, intercepting them on six occasions. On five of these, explosives which could have caused large-scale loss of life and/or major destruction had been recovered.
The Garda had been instrumental in preventing a bomb attack in London.
The security response in isolation was not enough in dealing with the threat from extremists, the Taoiseach said. "The Irish and British governments are working closely together. We are at one as to what is required. We will continue all our efforts, working closely with all of the parties involved to see the process through and to build a better future for everyone in these islands."
Making a special appeal to any young people who might be involved or thinking of becoming involved in violence, Mr Ahern said: "Listen to the voice of the Irish people. Ignore the siren voices of the depraved few who will ruin your lives, while using you to do their dirty work. These people are about as far from idealism as it is possible to be."
Opening a series of statements on the Omagh bombing, Mr Ahern said it was a little over two weeks since the atrocity, "since a street carnival was turned into a massacre, a ghastly relapse that joins and even surpasses the very worst tragedies of the last 30 years."
But even in 10 years - or more - the passage of time would have done little to heal what had been made to happen at 3.10 p.m. on Saturday, August 15th.
"As with previous outrages, survivors of the Omagh bombing will, years from now, still be suffering from their injuries; the bereaved will in many cases still be trying to come to terms with their loss; survivors and bereaved will still be troubled by thoughts of what might have been; and all those who responded so bravely and with such humanity at the scene will still be haunted at times by terrible images."