Labour leader Eamon Gilmore said that the 111,453 outstanding arrest warrants in the State represented the equivalent of a large five-seat constituency.
He said that the figure had been revealed to his party colleague, Tommy Broughan, in a parliamentary reply from Minister for Justice Brian Lenihan, adding that it was amazing that there were so many warrants for arrest issued by the courts and not yet executed.
Taoiseach Bertie Ahern, although not disputing the figures, suggested that in reality, the number of those evading warrants was small.
Mr Gilmore said that some 36,000 warrants, issued for the arrest of people who had not shown up in courts, had not yet been executed.
"The House will recall that Donna Cleary was the unfortunate woman who was shot through the window of her own home. She was killed by a man for whom a bench warrant had been issued, but who had not been arrested.
"In my constituency, when two gardaí were killed by a speeding car, one of the young men in the car that ran into the gardaí had a bench warrant issued against him, but he had not been arrested."
He added that almost 4,000 committal warrants had been issued by the courts, but the people involved have not been arrested.
Committal warrants were issued where somebody had been convicted by a court of an offence and a judge had decided that that person should be in prison.
"In other words, almost 4,000 people are out there, convicted of offences by the courts, with judges having decided they should be in prison, but they have not yet been arrested."
Mr Ahern said that while he would not dispute the figures provided in reply to a parliamentary question, he regularly saw figures relating to the number of people who evaded warrants on a weekly basis, which is a very small number.
He did not know how the question was categorised and had not read the details.
"Nonetheless, many people who are called and do not turn up on a particular day, for one reason or another, will turn up within a very short period, perhaps the following day or week or at the next court sitting.
"If I understand the deputy's point, we want to know the actual figure for people who entirely evade the judicial system or criminal justice system and do not turn up when a warrant is issued. Some of the cases relate to people for whom a warrant was issued and they either forgot about it or were sick and could not attend court but later turned up."
Mr Ahern said that the key figure related to those who had evaded the system, and that was not 36,000. He added that during the 30-year period of the Troubles, the number of outstanding warrants relating to people who did not turn up was approximately 20.
