At a news conference in Belfast on Wednesday, the Royal Ulster Constabulary and Garda Siochana renewed their appeal to the public to help them in their investigation.
Twenty-nine people died and more than 200 were injured on 15 August 1998 when the bombers left a massive car bomb in Omagh town centre.
The news conference was interrupted when Lawrence Rushe, whose wife Libby was killed, accused the authorities of a "conspiracy" in not preventing the bomb and not convicting the bombers.
It was the worst single atrocity in more than 30 years of the Troubles in Northern Ireland.
Speaking on the third anniversary of the atrocity, Superintendent James Baxter, the RUC's Omagh commander, and Garda Superintendent Tadgh Foley said only public help would help them "fill the gap" between what they knew and what they could prove.
'Conspiracy'
Lawrence Rushe, 72, said: "I have interrupted this because I came here to find the guilty.
"I am grieving my wife who was lost, my children who have lost a mother and grandchildren who have no granny. They have lost a beautiful person.
"I represent myself and, I hope, 30 other families. I am just disgusted by the lack of co-operation we have had from all levels.
"Are you a completely incompetent force?"
He added that the Real IRA said it was sorry for Omagh, but had continued its bombing campaign in Northern Ireland and London.
"I feel it is only a matter of time before these people kill again," he said.
Both Mr Baxter and Mr Foley vehemently denied that there was any conspiracy.
'We need evidence'
Superintendent Baxter said that after three years on the investigation, his officers were just as enthusiastic and determined to bring the bombers before the courts.
He said: "We are looking for help from the public and we feel there is a moral obligation on anyone who has information to bring that forward to bring those responsible to justice."
The Garda Commissioner, Pat Byrne, is among a number of senior policemen on both sides of the border who have said they know the identities of the dissident republican paramilitaries who carried out the bombing.
But Superintendent Foley said: "Knowing the names and suspecting people who have knowledge of people who carried out this atrocity is not enough. We need evidence to bring them before the courts".
'Republicans must help'
Michael Gallagher, from the Omagh Self-Help and Support Group, whose son Aidan died in the blast, also spoke at the news conference
He said he believed the knowledge that could convict the bombers "lay within the republican community" and appealed to "decent people" to contact the police.
Mr Gallagher said the families intended to keep putting pressure on the British and Irish Government, which, he said, had both given private and public assurances the bombers would be convicted.
He said the new terrorism legislation passed in both jurisdictions did not seem to have helped the investigation.
"We as a society need to ask ourselves: Has the effectiveness of the law become so blunted?" he said.
Mr Gallagher and other relatives of those who died have launched a civil action against five men with alleged links to the Real IRA.
They said they felt it was their last hope for justice.
Memorial service
On Wednesday, the injured and bereaved attended an interdenominational prayer service in the Garden of Remembrance in the town, constructed near the scene of the explosion.
RUC Chief Constable Sir Ronnie Flanagan and the garda commissioner attended the service.
Sir Ronnie said he wanted to reassure people that the "very active" police investigation would continue.
One man is currently awaiting trial in the Republic of Ireland accused of conspiracy to cause explosions.