Dr Diarmuid Martin was speaking at a prayer service in memory of the two men who were attacked and stabbed to death with a screwdriver in Drimnagh on February 23rd.
The event in the Church of Our Lady of Good Counsel was attended by President Mary McAleese, Minister for Justice Brian Lenihan and Minister of State Conor Lenihan.
The Taoiseach was represented by his aide-de-camp.
Pawel Kalite (26) and Marius Szwajkos (27) were fatally injured near their home in Benbulbin Road after a row involving a gang of youths.
The Archbishop appealed for a "community summit" - organised from the ground up - to address the question of violence in society.
Dr Martin said: "Parents, young people, teachers, priests, gardaí and others could work together on matters of common concern, sharing information and raising issues at the earliest opportunity.
"Much good work is already being done, and that work needs to be replicated around Dublin city and experiences and knowledge widely shared.
"Local authorities could offer practical support to such groups and bring them together. The prelate added: "The challenges of violence and substance abuse go beyond the realm of crime prevention and require a wider outreach to the entire community. We cannot just leave community involvement to moments of tragedy alone, when it is too late."
More than 2,000 people also attended a silent vigil near the scene of the attack on Saturday evening, including hundreds of locals and members of the Polish community.
Mr Lenihan said before tonight's service: "This is a tragic event and I would like to offer my condolences to the families of these two young men and my support to the community, who I know have been greatly affected by this tragedy."
Gardaí arrested a teenage girl today in connection with last weekend's double murder. Two male teenagers were released last week after being questioned in relation to the incident.
The family of Marius Szwajkos issued a statement following Saturday's vigil thanking everybody for their help and support.
"We are very grateful and appreciative of the number of condolences received from both Polish and Irish nationals over last few days who think of us in this time of sadness," the said.
"There are no frontiers for evil and right. We've lost a part of our life for ever, and it will no longer be the same. We would like to believe that the tragic death of two young men will not turn out to be senseless and will result in public discussion about the increasing level of aggression among the youth."
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