At a farewell ceremony at Ben-Gurion International Airport on Friday afternoon, Pope Benedict XVI showed he had taken note of the criticism that had been leveled at him earlier in the week - for saying that the victims of the Holocaust had been "killed" rather than murdered and for his failure to mention the Nazis as the perpetrators of that crime against humanity. Jews, Benedict said, were "brutally exterminated under a godless regime." One of the most solemn moments of his stay in Israel, he added, was his visit to Yad Vashem, where he had met some of the survivors "who suffered the evils of the Shoah." "Those deeply moving encounters brought back memories of my visit three years ago to the death camp at Auschwitz, where so many Jews - mothers, fathers, husbands, wives, brothers, sisters, friends - were brutally exterminated under a godless regime that propagated an ideology of anti-Semitism and hatred," he said. "That appalling chapter of history must never be forgotten or denied. On the contrary, those dark memories should strengthen our determination to draw closer to one another as branches of the same olive tree, nourished from the same roots and united in brotherly love." President Shimon Peres, in his farewell speech to the pontiff, said the pope had personally enhanced the visit with an additional spiritual dimension "by inspiring peace and elevating hope and understanding." He also expressed appreciation for Benedict's efforts to build bridges of mutual respect between people and nations, and castigated those extremist elements that use religion as a ploy for terrorism. Today's political and spiritual leaders, said Peres, face the profound challenge of finding a way to divorce religion from terror. He called Benedict's pilgrimage "a profound demonstration of the enduring dialogue between the Jewish people and the hundreds of millions of Christian believers throughout the world." In his farewell speech, the pope evoked memories of the late Egyptian president Anwar Sadat and prime minister Menachem Begin, when he said in relation to his quest for peace between Israel and the Palestinians: "No more bloodshed. No more fighting. No more terrorism. No more war." After a weeklong struggle to get his message across through a din of Israeli criticism and Palestinian protest against Israel, Benedict delivered his strongest words yet on the Jewish state's right to exist and the Palestinians' right to a country of their own. "Let it be universally recognized that the State of Israel has the right to exist, and to enjoy peace and security within internationally agreed borders," Benedict said on the airport tarmac before boarding a plane to Rome. "Let it be likewise acknowledged that the Palestinian people have a right to a sovereign independent homeland, to live with dignity and to travel freely," he said. "Let the two-state solution become a reality and not remain a dream." He called Israel's security barrier "one of the saddest sights" he had seen during his visit. Earlier on Friday, the pope made a stirring call for peace at Jerusalem's Church of the Holy Sepulcher. "The Gospel reassures us that God can make all things new, that history need not be repeated, that memories can be healed, that the bitter fruits of recrimination and hostility can be overcome," the pope said after kneeling in prayer beside the tomb of Jesus. Among other goals, Benedict's trip was meant to further the Roman Catholic Church's outreach to Jews and Muslims and support the beleaguered Christian communities of the Holy Land. The pope appeared to make headway on those fronts, though his visit lacked the historic resonance of his predecessor John Paul II's pilgrimage nine years earlier. During his eight-day visit, Benedict placed a handwritten prayer in the Western Wall, part of Judaism's holiest site. He took off his shoes to enter the Dome of the Rock, where Muslims believe the Prophet Muhammad ascended to heaven, and quietly prayed at the site of Jesus's birth. But there were reminders of Mideast strife at every step, and in the end Benedict's trip was as much political as it was spiritual. Benedict sat through a tirade by an angry Muslim cleric who commandeered a microphone at an interfaith meeting. He was subjected to a barrage of criticism in Israeli newspapers for his Yad Vashem speech. To get to Bethlehem, t he passed through an opening in the barrier Israel has erected in the West Bank. "As I passed alongside it, I prayed for a future in which the peoples of the Holy Land can live together in peace and harmony without the need for such instruments of security and separation," said Benedict, who called for an end to bloodshed and terrorism. Earlier Friday, Benedict entered the Church of the Holy Sepulcher escorted by black-robed clergy rhythmically banging staffs on the ground to announce his approach. He knelt and kissed the rectangular stone on which Jesus's body is said to have been placed after the crucifixion. Then he entered the structure that marks the site of Jesus's tomb and knelt inside alone, hands clasped, as priests chanted nearby.