Both Oglaigh na hEireann and the Real IRA have the type of bomb-making expertise described by the PSNI.
But so too does a group of disgruntled republicans recently believed to have defected from the mainstream IRA in Tyrone.
"We have real concerns about that area. There are serious concerns about leakage," a source with knowledge of intelligence assessments told this newspaper.
However, the source could not confirm if those who have left the IRA have merged with one of the dissident groups.
A senior republican speaking to this newspaper suggested dissidents may simply be trying "to sow confusion", but also pointed to the storm of condemnation that followed the weekend killing.
"It's interesting thus far that nobody has popped their head up to defend what happened or explain what happened," the source said.
"I don't think they anticipated the backlash," he continued.
"They probably hadn't thought about it. It may give them cause to think," he said.
But the source believed a statement would emerge from those responsible.
Yesterday police gave details of the bomb used in the weekend attack. Its components included high explosives and a tilt switch packed inside a plastic lunchbox.
It is a tactic used on scores of occasions by the IRA that has now been adopted by dissidents in their campaigns.
The North's government vowed last night that the killers of the PSNI officer would not drag Northern Ireland back to the past.
During an emergency statement to the Commons, Northern Ireland Secretary Owen Paterson branded the Omagh car-bombing "a revolting and cowardly act perpetrated by individuals intent on defying the wishes of the people".
But he pledged the PSNI would "not rest until these evil people are brought to justice".
Shadow Northern Ireland secretary Shaun Woodward warned of a "new generation" of terrorists who were "bordering on psychotic" adding that the "brutal assassination rekindles a deep wound" for the people of Omagh.
Meanwhile, it has emerged that Peter Robinson and Martin McGuinness are set to break new ground by attending the funeral of PSNI Constable Ronan Kerr together.
It will be the first time the North's leaders will have combined to pay their respects to a murdered member of the security forces, who was a Catholic.
Stormont's two most senior politicians believe the symbolism of their joint attendance will send a powerful message worldwide that they are united and determined to face down dissident violence.
Last night a former senior Catholic police officer said talks with dissidents should not be ruled out.
Peter Sheridan, who held the rank of assistant chief constable, said: "Raw emotions at the moment will not allow it to happen now, but the possibility of dialogue should be kept open."