Abbas was arrested by U.S. commandos during a raid early Tuesday morning on the southern outskirts of Baghdad. He had been convicted in absentia in an Italian court for the hijacking and sentenced to life in prison in 1986, but never served any time.
On Wednesday, Italian Justice Minister Roberto Castelli said Italy would seek his extradition.
A U.S. Embassy official described Thursday's meeting as a preliminary discussion. "Both parties recognize that it's a very complicated matter, which needs close further analysis," the official said.
Italian Justice Ministry officials said the meeting lasted two hours, and said more would follow. The meetings are intended to clear up legal questions surrounding Abbas' status and decide to which country Italy should address its extradition request.
No other details were released.
Castelli said Thursday that "whatever decision is made by the two countries, it will be made in full accord, without opening a confrontation."
Officials in Washington have said their first priority is to determine through interrogation whether Abbas can provide useful intelligence about Iraqi leaders and terrorist groups that might have been sheltered by Saddam Hussein. Other questions can be answered later, they said.
Abbas, whose real name is Mohammed Abbas, garnered international attention when the ship Achille Lauro was seized off Port Said, Egypt, by members of a PLO splinter group called the Palestine Liberation Front.
Hundreds of passengers, including American Leon Klinghoffer and his wife, were taken hostage. The hijackers demanded that Israel release 50 imprisoned Palestinians.
Militants shot Klinghoffer in his wheelchair and tossed him overboard.
The other passengers were released after a two-day ordeal and the commandos surrendered to Egyptian authorities, who put them on a flight to the PLO's headquarters in Tunisia.
U.S. Navy fighters forced the flight down in Sicily. The Italians, to the Americans' dismay, allowed Abbas to flee to Yugoslavia before a U.S. warrant for piracy and hostage-taking could be served.
Abbas disappeared, and international manhunts and a price on his head failed to flush him out. His faction relocated to Iraq after the attack.
Abbas does not now face U.S. charges in Klinghoffer's killing, although they could be brought at any time.