The Minister for Justice, Mr McDowell, has been accused of failing to prioritise the fight against the organised criminals behind Dublin's recent gangland murders.
The criticism followed the discovery on Thursday of the remains of the city's latest murder victim, 27-year-old Finglas man Mr Patrick Sheridan. His was the sixth gangland killing in the Ballymun and Finglas areas in the last six months.
The Garda Commissioner, Mr Noel Conroy, is due to appear before the Oireachtas Committee on Justice next week, where he will face questions about the spate of killings.
Labour's spokesman on justice, Mr Joe Costello TD, said the fact an estimated 15 people have been murder in gangland attacks since the beginning of the year proved criminal gangs now believed they can "kill at will". He added the murders "hardly seem to register" with Mr McDowell.
"I hope that it will not take the murder of another journalist or some other public figure before the Minister is shaken out of his complacency," he said.
"The real danger is that if the crime barons believe that they can get away with ordering the murder of associates or rivals without fear of prosecution it will be only a matter of time before they turn their guns on others."
A spokesman for Mr McDowell rejected Mr Costello's criticism. He said the Minister had already discussed organised crime with the new Garda Commissioner. "The Minister has full faith in the gardaí, but in the case of these killings investigations are difficult because of the lack of public cooperation."
Mr Sheridan, a father of two boys aged 3 and 6, was shot twice in the head. He had been missing from his home at Rathoath Avenue, Finglas, since last Monday. He was hooded when found at an area known as the Trench, Scribblestown Lane.
His body was concealed in thick undergrowth. Gardaí decided to search the area after they received a tip-off that a murder had been carried out in the Finglas area earlier in the week, and the body dumped.
The chief suspect for the killing is a drug dealer from Finglas, now living just outside the north inner city. He has been linked to at least one other murder in the Finglas area this year and is well know to gardaí, as are his associates.
Mr Sheridan was not a major criminal figure and it is not clear how he had fallen foul of the man suspected of his murder.
Det Insp Brian Sherry, who is leading the investigation, conceded Finglas has experienced a troubled period in recent months. He said while the people of Finglas had cooperated with gardaí in the past, it was "understandable they might get nervous when something of this nature is going on".
He said gardaí had not been slow to react to recent violence and had requested the Emergency Response Unit be drafted in three weeks ago to patrol the streets. The unit was maintaining a visible presence and was stopping and searching vehicles in a bid to disrupt criminal activity.