The statement by Mr Gerry Adams rejecting violence was welcomed by the Tanaiste. Describing it has "highly significant", Ms Harney said: "It is ground-breaking for the republican movement. It will be seen in time as a milestone in the evolution of the peace process."
She added that the attitude and intent demonstrated by Mr Adams's statement opened up new possibilities for dialogue and political progress.
"The key now must be for all of the main players to get down to the real business of making the Belfast Agreement work. The words of the agreement must now become a political reality. The full implementation of all aspects of the agreement will make a vital difference to the lives of all of the people of this island but particularly those of Northern Ireland."
Ms Harney said the Omagh bombing was so manifestly evil, so grievous in its human consequences and so crudely obvious in its timing and intention that it presented everybody with a challenge of unique urgency and importance.
"It was the work of a tiny perverted minority who reject the Belfast Agreement. Second only to the grotesque, immediate and continuing human misery caused, the cruellest aspect of the bombing was that it eclipsed the hope that flowed from the agreement and threatened a return to the abyss of the previous 30 years. It was as though the demon of violence, which we thought dead, had been revived in all its horror."
Ms Harney said all the words of condemnation and revulsion would ring hollow to the relatives and friends of the victims and to the body politic of the democratic world "unless the most powerful force of the law is unleashed against the perpetrators, sympathisers and fellow travellers of the self-styled, murderous `Real IRA' and their ilk".