Government and opposition politicians have called on the Continuity IRA, the only republican paramilitary group not to have called a ceasefire, to do so in the wake of the INLA ceasefire announcement.
However, the Taoiseach, Mr Ahern, warned yesterday that a "small element" of republican paramilitaries may not heed these calls and might attempt to continue a violent campaign. The Government would "ruthlessly suppress" any group that tried to do this, he said.
He also said he believed progress would be made soon on the decommissioning of paramilitary weapons. Welcoming the INLA's weekend ceasefire announcement, Mr Ahern said the Continuity IRA "must now acknowledge that it is insanity to defy the Irish people and must also definitively end their anachronistic campaign.
"The Government are determined to crush violence and ruthlessly to suppress any groups who persist in efforts to perpetrate it," he said. The INLA's statement was "good news at the end of a bleak and tragic week".
He warned that the Omagh bombing might not be the last atrocity, because of the activities of a "small element" who refused to accept the Belfast Agreement.
"I'd love to say to you that I believe this is the last event, as I would have loved to say it on a number of the last events," Mr Ahern told BBC's Breakfast with Frost TV programme yesterday. "But I think there is a small element, and they are small, who do not share that feeling.
"They believe that they have some kind of a mandate from some period in history that gives them some right to do this. Of course they have not. The people we have to deal with are the small element who have ignored that . . . and who have still said they are against the Good Friday agreement and will continue to pursue their actions."
Mr Ahern, who was interviewed straight after yesterday's memorial service for the 28 victims of the Omagh bomb, said he was confident the IRA would signal soon that they were ready to start decommissioning their weapons.
"I am confident that we will get to a position fairly soon where we will be able to move on beyond a lot of the rhetoric of the past and the harsh words and where these people will sit down, as per the agreement, and work together, and that we will deal with the decommissioning issue." The Minister for Foreign Affairs, Mr Andrews, also called on paramilitary groups not on ceasefire to announce an end to their violent activities. The will of the people, expressed in the two referendums North and South, was that the way forward on this island involved only peaceful, democratic means.
The Labour Party leader, Mr Quinn, welcomed in particular the "apologetic and contrite tone" of the INLA's ceasefire statement. "It clearly puts the spotlight on the remaining republican groups who have yet to declare full cessations. These groups are without a mandate or support."
The Sinn Fein chairman, Mr Mitchel McLaughlin, said politicians should use the INLA ceasefire as an opportunity "to forge ahead with the implementation of the changes which the people voted for in the Assembly elections.
"Any group not now on ceasefire should immediately announce an end to their campaign in order to allow the peace process to grow."