Palestinian President Mahmoud Abbas has invited Pope Francis to visit the Holy Land, matching an invitation from Israel.
The pontiff, who has made many appeals for peace in the Middle East since his election in March, has already told Israel he will visit and is widely expected to make the trip next year.
“I invited him to the Holy Land,” Mr Abbas said after a 30-minute private audience with the pope in the Vatican’s Apostolic Palace, their first meeting.
After the private part of the meeting, the pope gave Mr Abbas a pen, telling him “surely, you have a lot of things you have to sign”.
Mr Abbas responded: “I hope to sign a peace treaty with Israel with this pen.”
Both of Francis's two immediate predecessors, Benedict and John Paul, visited Holy Land sites in Israel and the Palestinian territories.
Most Christian Holy Land sites are in Israel but Bethlehem, the birthplace of Jesus, is in the Israeli-occupied West Bank, in the Palestinian territories.
The Church of the Holy Sepulchre, where Jesus is said to have been buried, is in East Jerusalem, which Palestinians want as part of their future state.
Mr Abbas and Pope Francis discussed the civil war in Syria and the prospects for peace between Israelis and Palestinians, the Vatican said in a statement.
Using the same language it used when Israeli President Shimon Peres visited Francis in April, the Vatican urged both sides to make "courageous and determined" decisions to move closer to peace, with the help of the international community.
Israeli and Palestinian negotiators began a new round of talks on Monday, picking up the tempo of their meetings at the request of the United States.
The two sides resumed direct peace negotiations in late July after three years of stalemate and have conducted a series of discussions far from the gaze of the media over recent weeks, without any outward hint of the slightest breakthrough.