Deputies last night expressed the hope that the formal inquiry into the fatal shooting by gardaí in Abbeylara, Co Longford, would report "as quickly as possible".
The Minister for Justice, Mr O'Donoghue, moved the formal establishment of the inquiry into the shooting of Mr John Carthy in April 2000, with provisions that it would report at the earliest opportunity and be as "economical as possible".
The resolution was formally agreed in the Dáil.
Calls were made for Mr O'Donoghue to consider locating the inquiry outside Dublin. Labour's deputy leader, Mr Brendan Howlin, suggested that it did not have to be in Dublin, while the Sinn Féin TD, Mr Caoimhghín Ó Caoláin (Cavan/Monaghan), said that it should be held in Co Longford, where the shooting occurred.
Mr O'Donoghue, moving the formal establishment of the tribunal of inquiry, said that he was not in a position to announce who would conduct the inquiry, but he hoped to make those arrangements "as quickly as possible".
The tribunal will investigate the fatal shooting by gardaí of Mr John Carthy at Abbeylara, Co Longford, in April 2000.
Fine Gael's justice spokesman, Mr Alan Shatter, hoped that the tribunal would reach conclusions and make recommendations within a "reasonable period of time".
Mr O'Donoghue said that the shooting had raised serious questions and issues which had to be answered.
The Minister pointed out that the use of firearms by the Garda was a relatively exceptional occurrence. The tradition of unarmed policing had been one of the great strengths of the Garda. When members of the force used arms, the "circumstances where this can occur are strictly regulated by the Garda authorities".
The tribunal will report to the clerk of the Dáil within four months of its establishment and as soon as possible after the 10th day of any oral hearings of the tribunal.
Mr Howlin said he regretted that the shooting had been an unresolved issue for so long because of the pain caused to the family of Mr Carthy and to the gardaí.
Mr Ó Caoláin said that Mr Carthy had been "treated as an armed enemy rather than as a man who needed help".