In their comments, ministers repeatedly pointed out that condemnation of the incident had been universal, by which they meant that, for the first time, Sinn Fein had said the same as all the other parties.
The Sinn Fein statement was faxed to the media under the heading: "Adams condemns Omagh bombing". It said: "Sinn Fein president Gerry Adams, who is breaking off his holiday following the bomb explosion in Omagh, has issued the following statement - 'I am totally horrified by this action. I condemn it without any equivocation whatsoever'."
The significance of this was not lost on ministers, who clearly regard it as a political advance of some note after all the years when Sinn Fein, under great pressure, resolutely refused to issue condemnations.
Opponents of the republicans will want far more from them than just words. The IRA arms-decommissioning issue has not gone away, and may intensify in the wake of the Omagh atrocity. Unionists are also pressing the IRA and Sinn Fein to declare that their war is over and that republicans will never again resort to arms.
There is also the question of "the disappeared", the dozen or more people that the IRA is said to have killed and secretly buried back in the 1970s. Their families are pressing for disclosure of their whereabouts so that they may be given decent burials, but republicans have yet to impart such information.
The Adams statement obviously did not deal with any of these issues, but it did have the immediate effect of blunting some of the inevitable post-Omagh criticisms of mainstream republicanism.
In the past, ministers would have been in the business of hammering him; this time round he was presented not as a pariah but as someone who had contributed something useful. He had included himself within society rather than excluded himself from the conventional political world.
His words therefore appear to have so far succeeded in sheltering Sinn Fein from much of the damage that might have been inflicted on it by a refusal to condemn the bombers. But they also have a deeper significance, in that they represent more than the crossing of a purely rhetorical Rubicon.
He has not said that all violence is wrong; he certainly has not said that IRA violence was wrong. But he has indicated that one type of republican violence is wrong, and this in itself represents a huge step in republican ideology.
The condemnation was tactically useful, but it also represents a commitment that cannot now be withdrawn: the "C word" has passed his lips and cannot be unsaid. None of this will have happened on the spur of the moment, for the Sinn Fein leadership is famously cautious.
Its new stance will be of value to it in the controversies that lie ahead in the peace process. The issue of prisoner releases will be the first of these, for the freeing of the first inmates under the provisions of the Good Friday agreement is due to take place in weeks.
While many will argue that these should be placed on hold, Sinn Fein will be insisting they should go ahead as planned. One question is whether there is a danger that any of those released might go off and join the Real IRA. This is highly unlikely.
The Secretary of State for Northern Ireland has a wide discretion to prevent the release of those supporting organisations that are not on ceasefire, which includes the Real IRA. There are in any event no prisoners in Northern Ireland aligned to the Real IRA or its associates, the Continuity IRA, and no strong indications that surreptitious supporters of these groups lurk within the ranks of mainstream IRA inmates.
Another controversy that will come to a head in the months ahead is that of Sinn Fein's inclusion in the executive that is to be formed to run the new Northern Ireland Assembly. The party insists that its numbers in the assembly entitle it to inclusion as of right, but many Unionists will oppose the idea of Mr Adams or his associates taking their place in a new administration.
The resolution of the present crisis will help to determine whether Sinn Fein does, in fact, go into government.
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