"You will be very welcome in Jerusalem and the holy places," Abbas told the Pope at the end of a private audience in the Vatican.
"Thank you very much," the German pontiff replied.
Israel captured Arab East Jerusalem in 1967 and annexed it as part of its capital in a move not recognised internationally.
Palestinians want East Jerusalem to be the capital of their eventual state.
East Jerusalem includes the walled Old City, site of major religious shrines from Judiasm, Islam and Christianity.
Abbas and the Pope spoke privately for some 20 minutes during an audience that was the highlight of a two-day visit to Italy and the Vatican.
Israeli President Moshe Katsav met the Pope last month and invited him to visit the Jewish state.
Benedict's predecessor, John Paul, made an historic trip to Israel and the Palestinian territories in 2000.
During that pilgrimage, the Pope asked the Jews for forgiveness for persecution by the Roman Catholic Church and also spoke of the suffering of the Palestinian people, calling for the creation of a Palestinian state.
During the public part of the audience a member of the president's delegation gave the Pope a passport from the Palestinian Authority as an invitation to visit Bethlehem, the birthplace of Jesus which is in the occupied West Bank.