The Pope also implored for divine comfort for "the families of the many victims of violence," in his address delivered before imparting the traditional blessing "urbi et orbi" (to the city of Rome and the world).
Some 100,000 people gathered in St. Peter's Square to hear the Holy Father's address, transmitted live on 84 television channels, after he presided at the Easter Mass.
"Men and women of the third millennium: Christ is risen, Christ is alive among us!" exclaimed the Pontiff, who later gave greetings in 62 languages, including Arabic and Hebrew.
May humanity find "the strength to face the inhuman, and unfortunately growing, phenomenon of terrorism, which rejects life and brings anguish and uncertainty to the daily lives of so many hardworking and peaceful people," he said.
"May the work of national and international institutions hasten the overcoming of the present difficulties and favor progress toward a more effective and peaceful world order," the Pope exhorted.
"May world leaders be confirmed and sustained in their efforts to resolve satisfactorily the continuing conflicts that cause bloodshed in certain regions of Africa, Iraq and the Holy Land," he added.
May Jews, Christians and Muslims, "who consider themselves children of Abraham," discover "the brotherhood that they share and that prompts in them designs of cooperation and peace," the Holy Father said.
"May the temptation to seek revenge give way to the courage to forgive; may the culture of life and love render vain the logic of death; may trust once more give breath to the lives of peoples," he said.
John Paul II concluded by praying to Christ "for the families of the many victims of violence."
"Help us to work ceaselessly for the coming of that more just and united world that you have inaugurated with your Resurrection," he said, before entrusting "this task" to the intercession of the Blessed Virgin Mary.
The icon of the Most Holy Savior, known as the "Acheropita" -- "not painted by human hands" -- was near the papal altar, a custom introduced during the Jubilee year 2000, recovering a tradition that had been lost for some 800 years. The icon is one of Christianity's most venerated images and is kept in the Sancta Sanctorum Chapel next to the Basilica of St. John Lateran.
Security measures were strict. Pilgrims entering St. Peter's Square had to wait in long lines before passing through metal detectors.
John Paul II, who was ending a Holy Week in which he presided over all the principal liturgical celebrations, looked well and spoke with a strong voice.