A gun amnesty will be part of the Criminal Justice Bill shortly due before the Oireachtas, the Minister for Justice said this afternoon.
"The provision is being made in the Bill for a gun amnesty so it's part of the package," said Mr McDowell.
He said he was introducing the measure following the weekend murder of Donna Cleary in Dublin early on Sunday morning.
Taoiseach Bertie Ahern today described the killing of Ms Cleary (22), who died after a gunman opened fire on a house party near her home in Coolock, Dublin shortly after 2.30am on Sunday, as a "new low". He said it was "hard to think of anything that can be much lower" than to spray the front room of a house with bullets indiscriminately.
He criticised what he described as "excessively lenient" jail sentences for those convicted of serious crimes.
"You see the amount of gun crimes and it does make you feel that perhaps we are just too lenient and people serve too short a sentence for murder," Mr Ahern said. "Too many people who commit murders get out after seven years and I just personally think that is ... too short."
Mr McDowell also condemned the killing. "This is a horrific crime, an innocent young mother shot by some savages who had a wanton disregard of life. Clearly if an automatic pistol is going to be used in circumstances such as these we all need to reflect on what kind of society we have and that applies to everybody, not just the Minister for Justice," he said.
"I would appeal to anybody anywhere in Ireland who knows of any firearm to think now about where all this possession of firearms is leading us. It's very very grave from the point of view of the quality of our life collectively that some people might think in a moment of bad spleen that they could take someone else's life just because they were refused permission to a party," the Minister said.
Five people are still being questioned in relation to the murder of Ms Cleary. The mother of a three-year-old boy was attending a 40th birthday party when she was shot dead.
The five - four men and a woman - were arrested in Co Kildare last night and are in custody at Santry, Whitehall and Coolock Garda Stations.
It is believed the shooting happened because four men, aggrieved at having been earlier refused entry to the party, returned with a pistol and shot indiscriminately into the house.
One garda said Ms Cleary appeared to be in the "wrong place at the wrong time". She was fatally wounded in the upper body by at least one of the shots and was pronounced dead at Beaumont hospital at about 4am.
Gardaí have stressed the shooting was not drug related and was not linked to any feud. A team of 50 detectives from Coolock, Santry and Clontarf Garda stations and from the National Bureau of Criminal Investigation have been assigned to the case.
Gardaí are asking anyone with information to contact Coolock Garda station at 01-6664200.
Green Party justice spokesman Ciarán Cuffe today reiterated his call for a gun amnesty on a "don't-ask-don't-tell" basis. "The senseless killing of a young woman on the over the weekend highlights the urgent need for action to stop the massive growth of illegally held weapons and the recent litany of related crimes," Mr Cuffe said.