The archbishop's comments come ahead of the May 24-26 planned visit by Pope Francis to the Holy Land.
"This wave of extremist actions of terror, are surely a grave concern to all reasonable persons. The government of Israel must be concerned, because it is very bad for the State of Israel's image abroad," the archbishop said in a statement.
Twal is calling on Israeli officials to arrest the vandals. "The actions are only drawing condemnation by Israeli leaders," he said, "but few arrests."
In response to the vandalism, which Israeli security forces have deemed "terrorism," Israeli Justice Minister Tzipi Livni convened an emergency meeting.
"'All that is necessary for the triumph of evil is that good men do nothing,' to use and often quoted line," cautioned the archbishop.