Fine Gael has called for the Taoiseach to consider appointing a special investigator of international repute to examine two central issues that left the Nally report not "fully finished".
The party leader, Mr Enda Kenny, also asked the Taoiseach to give as much information as possible from the report to the families of the Omagh victims, a request the Taoiseach is to discuss with the Minister for Justice, Mr McDowell.
Mr Ahern said: "One way or the other we will have contact again with the relatives, but we need to work out legally what we can give them."
He told the Dáil that with such reports, "personally, I would rather give everything but that is not possible and it is totally impossible in this case".
Large parts of the report cannot be published because of legal constraints and national security.
The authors investigated concerns about Garda activities in 1998, following an earlier report by the Northern Ireland Police Ombudsman, Ms Nuala O'Loan.
The Nally group inquired into allegations of Garda inaction on the Omagh bombing, ministerial interference in the judicial process and unlawful and improper conduct by senior Garda officers.
The Minister for Justice told the Dáil on Wednesday that the report concluded there was no foundation to the allegations the group investigated.
Raising the two "central issues" in the investigations, Mr Kenny said that the person central to the entire report, the informant, was not questioned and that when questions were submitted to him through his legal adviser, they were not answered.
The Fine Gael leader also said there was a "divergence of opinion on the intelligence level and information available to the PSNI and the Garda in respect of certain aspects of the Omagh" bombing.
Mr Kenny asked if the Taoiseach would ask the Nally group to re-examine the two issues or, "as they are not professional investigators, could consideration be given to bringing in a professional investigator of international repute to examine those two issues?"
Mr Ahern confirmed that the individual concerned, who was not questioned, "has on legal advice not co-operated with the group".
However, the Taoiseach rejected suggestions that the group promised that before completing the report, the investigators would go back to the Northern Ireland Police Ombudsman, whose information, intelligence and evidence led to the commissioning of the report.
Mr Ahern said that the members of the group confirmed that no undertaking was given to the Police Ombudsman that she would be contacted again about the report.
"In fact, the group made it clear to the Ombudsman that its function was to report to the Minister for Justice and nothing else. No undertaking was given in any form to return to the Ombudsman."
Appealing for information to be given to the relatives, Mr Kenny asked that the Taoiseach and Minister for Justice would meet the relatives of the victims of the bomb, explain the Nally report to them "and at least give them that comfort and a sense of interest in understanding the depth of grief that these families still experience".
