There have been calls for an independent inquiry into the fatal shooting by gardai of John Carthy outside his Co Longford home this week.
The Irish Council for Civil Liberties said the Abbeylara case was "not isolated", adding that the failure to publish details of Garda policy on the use of force rendered the current investigation "meaningless".
A number of politicians expressed disquiet at the secrecy surrounding the internal Garda inquiry, announced by Garda Commissioner Pat Byrne and headed by Chief Supt Adrian Culligan from Cork.
Fine Gael's justice spokesman Mr Jim Higgins said it was "vitally important" that the findings of the inquiry be published.
The standard Garda manual states: "In order that a discharge of firearm may be justified for any particular case it must be shown that the intention of the member firing was to attempt a legal purpose and that all other means of achieving this purpose had been exhausted before firing."
However, Mr Higgins said it was not clear whether Garda policy demanded officers to initially attempt to wound a target rather than kill.
A Garda spokesman said such rules of engagement were an "internal matter" and not available to the public.
He said, however, they would be studied in the context of the internal investigation to see whether any change in the rules was needed.
Socialist Party TD Mr Joe Higgins said an independent inquiry should be launched immediately to run in tandem with the Garda inquiry.
"The fact that the media was kept back from the scene and did not see what happened makes it all the more important to have an open inquiry."
He added: "What is incomprehensible about his whole thing is that the gardai did not seem to have any contingency plan for dealing with a disturbed man with a shotgun.
"One would have thought he could have been incapacitated, or wounded, or somehow stopped without being killed."
The Labour Party spokesman on justice, Mr Brendan Howlin, said, "No Garda operation that ends in the loss of life, even in circumstances such as these, can be called a success. It is imperative now that we get to the bottom of events at Abbeylara.
"Early publication of the results of the Garda inquiry by the Commissioner and the Minister for Justice will facilitate a proper debate on the use of appropriate force by the gardai in siege situations.
"At that point, we will be in a better position to determine whether further action is necessary."
The director of the Irish Council for Civil Liberties, Mr Donncha O'Connell, criticised the lack of transparency in Garda policy.
"The fact that the guidelines for the use of force are not in the public domain renders any subsequent investigation into the use of force meaningless. How are we to know whether adequate safeguards were observed when we do not know what safeguards, if any, exist in the guidelines?"
He said a further difficulty with the inquiry was that it would be conducted without any external supervision.
"This contrasts with the approach taken to the tragic killing by the RUC last week of James Cornwell in Newtownabbey. In that case, the police investigation will be supervised by the Independent Commission for Police Complaints."
