The call by Archbishop Sean Brady came after two police officers and a motorist narrowly escaped death in a double mortar bomb attack in County Down, and a police patrol foiled a similar attack in Londonderry.
Archbishop Brady said: "I think it takes great courage to negotiate, probably more courage than maybe to do acts of violence. I would appeal to people to think about that. There is no road through violence ... The only way forward is through dialogue and negotiation and it will have to come some day."
Two mortar bombs were fired simultaneously from a twin-tube launcher at an Royal Ulster Constabulary car on the outskirts of Downpatrick late on Saturday night. The missiles just missed the vehicle, and a woman driving in the opposite direction. Ronnie Flanagan, chief constable of the RUC, said the attack was carried out with "total disregard" for the lives of civilians.