Responding to the attempted car bombing of an off-duty PSNI constable in Belfast on Monday and the discovery of a pipe bomb near a police station in Co Armagh, Dr Diarmuid Martin said the humility of the Christmas story was the very opposite of the arrogance of dissidents and criminal gangs "who feel that they can just take lives in that way".
Warning that "this is not the way to build peace", the archbishop said the dissidents had "lost contact with their faith, if they have a faith" and "they have lost contact with their ideals".
Dr Martin added that it was clear the people of the island of Ireland wanted a peaceful coming together and that splinter republican elements were responsible for creating an "unhealthy climate".
Dissidents
He was speaking after a Mass to mark the World Day of Peace attended by President Michael D Higgins, representatives of the Oireachtas and the European Parliament, diplomats, members of the papal orders and representatives of the Garda and the Defence Forces.
Fine Gael former presidential contender Gay Mitchell, who attended the Mass, described the dissidents as "fascist" due to their belief that they could take people's lives and dictate to the government, parliament, the army and the police north and south of the Border.
"It is an unbelievable and abominable arrogance to appoint themselves in this way," he said, adding that the people of Ireland, north and south, had spoken in a referendum and decided what the future would be.
He added: "Nobody is going to bomb or bully us into a different way, and I do think on this day of peace that it is something we should be reflecting on."
Separately, the Papal Nuncio, Archbishop Charles Brown, who celebrated the Mass having just returned from Christmas holidays at home in the US – where he said people were still in shock over the Newtown massacre in Connecticut – called for tighter gun control laws in America.
He told the Irish Independent: "It was one of the most horrific things that has happened in the US for a long time. Anything that can be done to prevent such things from happening needs to be done, and if legislation on better control of firearms can do that, then it certainly needs to be done."
He acknowledged there were "many things that need to be re-evaluated in light of this horrific tragedy", including violence in society and the isolation that is part of modern suburban American life.