Joaquin Navarro-Valls, the Vatican spokesman, declined to elaborate on what the pontiff said the Palestinians must do to bring about peace.
Violence marred primary elections across the Palestinian territories earlier in the week, but Abbas told reporters Saturday that he was working to "bring calm" to the region. Abbas also said that the pontiff with his "symbolic weight ... can carry out a decisive role for peace" between Israel and the Palestinians.
At the end of their private 20-minute meeting in Benedict's library, Abbas invited the pope to visit the Holy Land, saying he would "be very welcome in Jerusalem and all the holy places." Benedict thanked him for the invitation.
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.
Jerusalem is a thorny issue in Israeli-Palestinian relations. Palestinians hope for an independent state that would include traditionally Arab east Jerusalem, which Israel captured in the 1967 Middle East war. Benedict's predecessor, Pope John Paul II, who visited the Holy Land in 2000, had called for Jerusalem to be a kind of open city, with no single state having sovereignty.
The Vatican also said Saturday's talks covered the state of Catholics living in the Palestinian territories. Catholics, who comprise 1 percent of the population in Israel and the territories, have faced violence and restrictions in movement, sometimes not being able to visit the sacred sites where Jesus once worked.
Abbas said he briefed the pontiff about the conditions in which Palestinians, especially Christians, live. "I asked for his support and help in easing the difficult problems that the Palestinian people suffer," Abbas said.
When Pope John Paul II received the Palestinian leader Yasser Arafat in 1982, the first of many meetings between the two men, it sparked protests in Israel and the worldwide Jewish community. John Paul consistently championed rights for Palestinians while at the same time greatly improving the Vatican's relations with Israel.
Abbas' visit to the Vatican was his last major appointment in 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.