The Derry clergyman made the call during a Mass for 'the disappeared' in Armagh on Palm Sunday.
He called on anyone with knowledge about the cases to contact the Independent Commission for the Location of Victims' Remains.
"Today I appeal again to the conscience of anyone who can help with the cases of Joe Lynskey, Robert Nairac, Seamus Ruddy and Columba McVeigh to bring even the slightest clues to the Commissioners' attention so that the agonising wait of the remaining families can be shortened and their loved ones can at last have a Christian burial," he said.
During his homily on Sunday, the Archbishop acknowledged many people were complicit in terrible deeds throughout the Troubles.
"There are people on all sides who carry secrets - memories of their own involvement in the deaths and injury of thousands of men, women and children.
"In some cases they pulled the trigger, planted the bomb, blindly followed orders or gave the command for death or punishment.
"In other cases they willingly drove a car, kept watch, spread fear, collected money or information, sheltered combatants, colluded or covered up, destroyed evidence or intimidated witnesses. These were awful, terrible times."