They say the Government has failed to co-operate with the civil action the families are taking against five individuals.
But a government spokesperson rejected the accusation, saying it has been in continuing contact with the families’ solicitors.
The victims’ families are seeking £14 million (€18m) in compensation from Michael McKevitt, who is currently serving a 20-year sentence for directing terrorism, and four other men.
The case is due to begin in the High Court in Belfast in just under a fortnight.
Speaking on RTÉ’s Prime Time programme last night, the families said evidence crucial to their case was held by the Garda Síochána but had not yet been released.
This was despite a promise by Mr Ahern that his Government would do “everything we can to assist in bringing the perpetrators of this terrible crime to justice”.
Last night, families’ spokesman Michael Gallagher said: “If the Dublin Government is serious about dealing with terrorism in this country, what they will have to do is stand up and be counted and, sadly to date, they have not done that.
“We have had continuous promise after promise, even from the Taoiseach himself last week saying they would do everything possible. But in reality the substance is very little, because we are still waiting,” he said.
But the Government said it categorically rejected any suggestion that it was “dragging its feet” in dealing with the requests of the legal representatives of the Omagh relatives.
“There have been ongoing contacts between the Department of Justice, Equality and Law Reform and H2O, the solicitors representing the families taking the civil action,” a Government spokesperson said.
“While the frustrations of the relatives are appreciated and regretted, there is a legal process under way involving the court and the parties to the action. The department [of justice]... must follow proper legal procedure and failure to do so could leave open a legal challenge from the defendants in the proceedings.”