Abbas, who is on a tour of Europe to thank countries that supported the November 29 resolution by the U.N. General Assembly recognising Palestine, held private talks with the pope for about 25 minutes in the Vatican's Apostolic Palace.
"It is hoped that (the resolution) will encourage the commitment of the international community to finding a fair and lasting solution to the Israeli-Palestinian conflict, which may be reached only by resuming negotiations between the parties, in good faith and according due respect to the rights of both," a Vatican statement said.
The 193-nation General Assembly overwhelmingly approved a resolution to upgrade the Palestinian Authority's observer status at the United Nations from "entity" to "non-member state," the same status as the Vatican.
The Vatican welcomed the resolution, which amounted to an implicit recognition of a Palestinian state.
But at the time the Holy See also renewed its call for an internationally guaranteed special status for Jerusalem, something which Israel rejects.
Israel captured East Jerusalem - along with the West Bank and Gaza Strip - in the 1967 Middle East war and later annexed it in a move not recognised internationally. The Jewish state now regards Jerusalem as its "united and eternal" capital.
Palestinians want East Jerusalem to be the capital of a state they seek in the West Bank and Gaza and agree with the Vatican that the city needs international guarantees.
Israel has always maintained that it already guarantees Jerusalem's special nature as sacred to the three great monotheistic religions - Christianity, Judaism and Islam.
Israel withdrew from Gaza in 2005 but is steadily expanding settlement in the larger West Bank.
The Vatican said the pope and Abbas also discussed the "situation in the region, troubled by numerous conflicts," which was seen as a clear reference to the civil war in Syria.
Abbas later met Italian Prime Minister Mario Monti, who expressed the Italian government's support for the construction of a Palestinian state, his office said in a statement.
Abbas was also due to meet Pier Luigi Bersani, the head of the Democratic Party, which is widely expected to win national elections early next year.
Italy's centre-left has traditionally supported Palestinians while the centre-right has been closer to Israel.