One day after the capture in Iraq of the wanted Palestinian terrorist Abu Abbas, American officials Wednesday began weighing several options for handling him.

The three scenarios being discussed included holding him at a military base, bringing him to the United States for possible prosecution or transferring him to a third country.

The situation is full of possible entanglements.  The Palestinian Authority said it wants Abbas freed.  Italy, which convicted him in absentia for masterminding the 1985 hijacking of the cruise ship Achille Lauro, announced it would seek his extradition.

Future plans aside, U.S. officials viewed Abbas' capture as a major victory in the war on terrorism, as well as a vindication of President Bush's claim that Saddam Hussein's regime was harboring terrorists.

"This mission success highlights the U.S. and our coalition partners' commitment to defeating terrorism worldwide," U.S. Central Command said in a statement. "The capture of Abu Abbas in Iraq removes a portion of the terror network supported by Iraq and represents yet another victory in the global war on terrorism."

Abbas was captured early Wednesday morning in Baghdad by American special operations forces supported by the Army's 3rd Infantry Division.

Abbas had tried twice to flee to Syria in recent days but was turned away at the border, Palestinian officials close to the guerrilla leader's organization said Wednesday. He also reportedly tried to escape to Iran.

After the fall of Baghdad last week, Abbas traveled to the northern Iraqi city of Mosul, then to the nearby Syrian border, but was recognized and turned back by Syrian officials, the sources said.

He returned to the Syrian border several days ago after Palestinian factions based in Damascus tried to intercede on his behalf, but was rebuffed again.

Abbas returned to Baghdad and was captured the next day, the sources said from south Lebanon.

The raids on Baghdad hideouts of Abbas' branch of the Palestine Liberation Front also yielded other suspects and weapons including rocket-propelled grenades, Yemeni and Lebanese passports and other documents.

Abbas' American captors were sure to grill him about his ties to other terror groups and Saddam Hussein, who sheltered him for years.

"Justice will be served," said Marine Maj. Brad Bartelt, a spokesman for Central Command.

His interrogators also would want more information about the October 1985 hijacking of the Achille Lauro in the Mediterranean, during which an elderly American passenger, Leon Klinghoffer, was shot to death and dumped overboard in his wheelchair.

Abbas was never aboard the Achille Lauro, but his PLF faction carried out the hijacking.

"He got away from us, and we've been chasing him ever since," said Vince Cannistraro, a former CIA counterterrorism chief. "He's a big catch for us. It's an old score to settle."

The Palestinian Authority on Wednesday demanded his release, saying the arrest violated a 1995 agreement between Israel and the Palestinians that was signed by then-U.S. President Clinton.

No PLO officials were to be arrested for violent acts committed before the 1993 Israel-PLO pact of mutual recognition, the Palestinians said.  Abbas' branch of the PLF renounced terrorism after the 1992 Israel-PLO Oslo Accords, and the group is believed to be politically close to Yasir Arafat's Fatah organization.

A Palestinian Cabinet minister, Saeb Erekat, said Abbas has visited Palestinian areas repeatedly since 1996 with Israeli and U.S. acquiescence.  After the Oslo Accords, Abbas lived openly in the Gaza Strip for several years.

Italian Justice Minister Roberto Castelli said Wednesday his country would seek Abbas' extradition.

"Now we know he has been captured in Iraq, but that he's in the hands of American authorities. We will have to clarify some legal questions as to whom to request the extradition, which we'll do as soon as possible," he said.

U.S. special forces had been looking for Abbas for a few days, searching several locations before finding him, Fox News has learned.

In the early hours of Wednesday morning, a suspect was finally caught who "subsequently admitted to being Abu Abbas."

He was captured with documents, weapons and money — "tens of thousands of dollars," according to one official.

Leon Klinghoffer's daughters, Lisa and Ilsa Klinghoffer, said Wednesday on NBC's Today show that they wanted Abbas to face trial in the United States.

"We want him brought here, and we want him tried here, in our country, and we want to know that he's going to serve his full sentence, which is hopefully a life sentence," said Lisa Klinghoffer.

Abbas and his small faction had been relatively quiet in the decade after the Achille Lauro hijacking, and he repeatedly expressed regret for it.  Most of the group's other terror attacks involved penetrating Israeli borders by sea or air, and most ended in failure.  Its support among Palestinians in the occupied territories was believed to be nonexistent.

But in recent years, the Abbas wing of the PLF served as a conduit for Saddam Hussein's payments to the families of Palestinian suicide bombers, payments which totaled about $35 million.  Israeli officials also accused Abbas of training would-be terrorists at Iraqi camps.

President Bush cited the presence of Abbas in Baghdad in an October 2002 speech outlining the arguments for removing Saddam from power.

"Iraq has ... provided safe haven to Abu Abbas, who was responsible for seizing the Achille Lauro and killing an American passenger," Bush said. "And we know that Iraq is continuing to finance terror and gives assistance to groups that use terrorism to undermine Middle East peace."

Four PLF guerrillas seized the Achille Lauro as it sailed from Egypt to Israel in October 1985. They demanded the release of 50 Palestinians from Israeli prisons.

After several days, they shot Klinghoffer, 69, then tossed him and his wheelchair overboard.

The hijacking ended after negotiations involving Egypt and the PLO. Abbas, who helped negotiate the surrender, and the four hijackers were flown out of Egypt on a jet that was intercepted by U.S. Navy fighters and forced to land in Sicily.

Armed U.S. and Italian soldiers faced off, each demanding custody of the hijackers. The situation was resolved after feverish telephone calls between Premier Bettino Craxi and President Reagan.

The Italians took custody of the four and promised to try them, but refused to detain Abbas, saying Washington's evidence was insufficient and that he held an Iraqi diplomatic passport. Within two days, he slipped out of the country.

Two weeks later, Italian magistrates filed charges against Abbas and issued an arrest warrant, which has remained outstanding.

In June 1986 he was convicted by an Italian court in absentia and sentenced to life imprisonment. The sentence was upheld on appeal.

Abbas was a member of the Palestine Liberation Organization's executive committee from 1984 but left in 1991, according to the State Department.

Fox News' Jim Angle and The Associated Press contributed to this report.