JERUSALEM—Hamas and Hezbollah, groups that have long battled Israel with violent tactics, have begun to embrace civil disobedience, protest marches, lawsuits and boycotts—tactics they once dismissed.

For decades, Palestinian statehood aspirations seemed to lurch between negotiations and armed resistance against Israel. But a small cadre of Palestinian activists has long argued that nonviolence, in the tradition of the American civil rights movement, would be far more effective.

Officials...