The 32 County Sovereignty Movement, in a statement last night, said it was "shocked and devastated" by the Omagh bombing but categorically rejected any suggestion it was responsible.
Security sources say the movement is the political wing of the "Real IRA", a claim the group denies. The movement was formed late last year after resignations in republican ranks over the peace process.
Its chairman is an expelled Sinn Fein councillor in Omagh, Mr Francie Mackey, and its leading spokeswoman is Ms Bernadette Sands McKevitt, sister of dead IRA hunger-striker, Bobby Sands.
A spokesman for the group said it would not be giving media interviews but he read out a short statement: "We are deeply shocked and devastated by the terrible tragedy in Omagh, Co Tyrone.
"We share the grief and sorrow of everyone on the island of Ireland and we offer our sincerest sympathy to the injured and the bereaved and their family and friends at this moment in time.
"The killing of innocent people cannot be justified in any circumstances. We are a political movement and not a military group. We reject categorically any suggestion that our movement was responsible in any way." The spokesman said the group had no further comment to add.
No organisation has so far claimed responsibility for the attack but republican sources yesterday had little doubt the "Real IRA" was involved.
They pointed to similar patterns between events last weekend and those on a Saturday afternoon a fortnight earlier when the "Real IRA" bombed Banbridge, Co Down.
Hours after the Omagh bomb, incendiaries were found in premises in Belfast and Coleraine, Co Derry. Dissident republican sources said they were "stunned" when they heard about the Omagh bomb.
They denied there could have been any intention to kill civilians.
"It would make no sense to do that," one said. "The people killed are the very people who republicans would be looking to for support. This bomb has not helped the republican agenda. Instead, it has played directly into the hands of those who wish to demonise republicans."