Mr Justice Henry Barron is due to report on the Dublin bombings of 1972 and 1973 as well as many other pre-1974 bombings and the murders of Brid Carr in 1971, Oliver Boyce and Brid Porter.
He will then publish a separate report on the murder of Seamus Ludlow in Co Louth in 1976.
The third report on later cases, including the Dundalk bombing of 1975 and the Castleblayney bombing, may be finished by the end of the year, Mr Ahern told the Dail.
Justice Barron published his first report - an investigation into the 1974 Dublin and Monaghan bombings - in December.
Mr Ahern told the Dail that the senior judge's work on the second report was "well advanced. I understand he has most of the drafting done and he just has some outstanding contacts to make," he said.
"That will cover a number of cases the two bombings in Dublin in 1972 and 1973, the Clones, Belturbet and Pettigo bombings in 1972 and the other bombing incidents that took place before May 1974.
"I understand Justice Barron will report next at the beginning of June. The third report will be much later."
Both reports will be put to a joint parliamentary committee for a full inquiry.
Mr Ahern also revealed he had spoken to British Prime Minister Tony Blair this weekend about the possibility of conducting a judicial investigation into the 1974 Dublin and Monaghan bombings in Northern Ireland or Britain.
He said he had not been informed of an official British government position.
PA