Mutual respect and the support of the international community will be an important part of any agreement, the statement said.
The situation of the dwindling Christian community in Palestine was also discussed, along with the contribution the region's Christians make "to social life and to peaceful coexistence among peoples," the Vatican statement said.
Reporters heard the pope ask Abbas, in English, about his meeting in New York last month with U.S. President Barack Obama and Israeli Prime Minister Benjamin Netanyahu. Reporters did not hear the Palestinian's reply.
The pope and Abbas spoke privately for 15 minutes before the president introduced his eight-man delegation, which included Saeb Erekat, the chief negotiator on issues with Israel. Abbas introduced him to Pope Benedict as a man with "a very important job."
In the customary exchange of gifts, Abbas gave the pope a painting of Jerusalem on ceramic, with the caption in English and Arabic: "Jerusalem Capital of Arab Culture."
The pope gave Abbas a bas relief in pewter of St. Peter's Square surrounded by a circular ivory ceramic frame.
Abbas later met with Cardinal Tarcisio Bertone, Vatican secretary of state.
Pope Benedict supports a two-state solution for the Israeli-Palestinian conflict. He met both Abbas and Netanyahu in private meetings during his trip to the Holy Land in May.
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