The government has ruled out holding talks with dissident republicans following the murders of two soldiers and a policeman.
Catholic priest Father Aidan Troy suggested dialogue with the factions could "prevent future loss of life".
However, Northern Ireland Security Minister Paul Goggins said dissidents had no role to play in politics.
"There is a political process in Northern Ireland and those who believe in democracy have joined it," he said.
"Dissident republicans have singularly failed to join it, they are trying to undermine it.
"In fact, it's the very success of it which they are seeking to undermine and attack."
Fr Troy said channels of communication could be opened in order to "say this is absolutely, unconditionally wrong."
"There isn't going to be any appeasement in this approach but if it saves one other grieving family, and even if people were to pour scorn on me today, I don't mind that," he said.
Last Saturday, the Real IRA shot dead Sappers Mark Quinsey, 23, from Birmingham, and Patrick Azimkar, 21, from London, at Masserene barracks in Antrim as they accepted a pizza delivery.
Four men were also injured in the attack.
Two days later, the Continuity IRA murdered Constable Stephen Carroll in Craigavon.