The ship was commandeered by Abbas' small Palestine Liberation Front. Palestinian militants threw an elderly wheelchair-bound Jewish American tourist, Leon Klinghoffer, overboard.
Abbas was captured in Iraq in April by U.S. forces. Late Tuesday, officials in Palestinian leader Yasser Arafat's office, speaking on condition of anonymity, said that Abbas had died in U.S. custody.
In Washington, a U.S. official, also speaking on the condition of anonymity, said Abul Abbas died recently of natural causes while in U.S. custody. The official said his health had been deteriorating.
When Abbas was captured, the Palestinian Authority demanded his release, saying the United States had pledged not to prosecute him as part of a blanket promise not to press charges against Palestinians who acted against Israel before interim peace accords were signed in the 1990s.
The United States also endorsed a 1995 interim peace dea which grants PLO members immunity for violent acts committed before September 1993, when the two sides signed a mutual recognition agreement.
The 55-year-old Abbas has been a marginal figure in the PLO. He was a member of the PLO's executive committee, but left in 1991. His tiny faction has very few followers in the West Bank and Gaza Strip. According to Israel's Shin Bet security service, the PLF has sent some members to Iraq for military training.
In April 1996, Abul Abbas visited Gaza for the first time, as part of the amnesty offered by Israel. At the time, he apologized for the killing of Klinghoffer.
In 1998, he returned to attend a session of the Palestine National Council, the Palestinians' parliament-in-exile, for a crucial vote on abrogating chapters of the PLO founding charter calling for Israel's destruction. In the end, Abul Abbas did not participate in the vote.
At that time, Israeli attorney general Elyakim Rubinstein said Abul Abbas did not pose a threat to Israeli security, and that it would be unreasonable to prosecute him for acts committed before 1993.
U.S. commandos caught Abbas last April during a raid on the southern outskirts of Baghdad.
Abbas had been convicted in absentia in an Italian court for the 1985 hijacking and sentenced to life in prison in 1986, but never served any time. His arrest came 18 years after his crime.
Abbas became an internationally known figure with the seizure of the Achille off Port Said, Egypt.
During the hijacking the Palestinians demanded that Israel release 50 imprisoned Palestinians, and 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 PLO 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. He next turned up in Gaza where he renounced terrorism.