"You will be very welcome in Jerusalem and all the holy places," Abbas, speaking English, told the pope after their private 20-minute meeting in Benedict's library.
"Thank you very much," the pope replied.
Abbas later told journalists that Benedict "responded positively" to his invitation but indicated no date for a visit. Last month, Israeli President Moshe Katsav invited Benedict to Israel and said he hoped the pope would visit next year.
During their meeting, Benedict and Abbas talked about the Israeli-Palestinian conflict, with the pope stressing "the need to integrate all components of the Palestinian people into the peace process," Vatican spokesman Joaquin Navarro-Valls said in a written statement.
The statement did not elaborate but appeared to be a reference to extremist elements blamed for violence and terrorism. Violence marred primary elections across the Palestinian territories earlier this week.
Briefing journalists at a Rome hotel, Abbas said the pope with "his symbolic weight ... can carry out a decisive role for peace."
One of the members in the Palestinian delegation presented the pope with a document that Abbas later said was fashioned by Bethlehem's inhabitants "to express the ties of friendship and spirituality that link the Vatican and the people of Bethlehem, dear to Christians as Jesus' birthplace."
When Pope John Paul II received Palestinian leader Yasser Arafat in 1982, the first of many meetings between the two men, it sparked protests in Israel and in the worldwide Jewish community. John Paul consistently championed rights for the Palestinian people while at the same time greatly improving the Vatican's relations with Israel.
Abbas' visit to the Vatican, which included separate talks with the pope's secretary of state, Cardinal Angelo Sodano, was his last major appointment of a three-day visit to Italy.
At a joint news conference Friday with Italian Premier Silvio Berlusconi, Abbas praised Israeli Prime Minister Ariel Sharon and expressed confidence that the Israeli people would choose the path of peace in elections scheduled for March.
He also promised "security and transparency" in next month's Palestinian parliamentary elections.