Abbas, who had moved to Iraq to escape the reach of American law enforcement, is wanted for the murder of Leon Klinghoffer, a wheelchair-bound American passenger who was shot and tossed overboard.
Lisa and Ilsa Klinghoffer, the daughters of Leon Klinghoffer, say the arrest of Abul Abbas will send a message to other terrorists.
CBS News Correspondent David Martin reports Abbas was taken into custody by American special operations forces during a raid Monday night on the outskirts of the capital city.
Officials also say several associates of Abbas were detained during raids at several sites around Baghdad. Commandos, tipped off by U.S. intelligence to Abbas' whereabouts, seized documents documents - including Yemeni and Lebanese passports — and weapons such as rocket-propelled grenades.
The man known as Abul Abbas, whose name actually is Mohammed Abbas, led a faction of the Palestine Liberation Front, a Palestinian splinter group.
American officials would not say whether Abbas will be held inside Iraq, taken to a third country or detained at a U.S. base. They also would not say whether he would face charges in the United States. Abbas was sentenced in absentia to life in prison in Italy for masterminding the Achille Lauro hijacking.
His faction operated out of Tunisia until the October 1985 attack on the Achille Lauro, after which it relocated to Iraq. His group was also responsible for some attacks in Israel.
"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 PLF faction under Abbas was a conduit for Saddam Hussein's payments to the families of Palestinian suicide bombers. Israel's Shin Bet intelligence service reported earlier this year that Israel captured several Palestinians who trained at a PLF camp in Iraq and were told by Abbas to attack an Israeli airport and other targets.
Abbas, either 61 or 62, had eluded arrest since four of his followers hijacked the Achille Lauro as it sailed from Egypt to Israel in October 1985. They demanded that Israel release 50 imprisoned Palestinians.
During the hijacking, his followers shot and killed Jewish American passenger Leon Klinghoffer, 69. The hijackers then tossed Klinghoffer and his wheelchair off the cruise ship.
Klinghoffer and his wife, Marilyn, along with nine friends from the New York area, took the cruise to celebrate their 36th wedding anniversary. They were among 500 passengers taken hostage. Klinghoffer's wife died of cancer just four months after the hijacking.
The hijacking ended Oct. 9 after Egypt negotiated with the hijackers. 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.
Tensions arose as soon as the plane landed. Armed U.S. and Italian soldiers faced off, each side demanding custody of the hijackers. The situation was only 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 the evidence compiled by Washington 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 tried in absentia, convicted and sentenced to life imprisonment for masterminding the hijacking. The sentence was upheld on appeal.
In an interview last November with The New York Times, Abbas denied responsibility for the death of Leon Klinghoffer. "Of course, it wasn't my fault. I didn't shoot the man," he said. "But he was a civilian, and I ask myself, 'What was his fault?'"
Abbas also condemned the attack on the World Trade Center and spoke contemptuously of Osama bin Laden and al Qaeda.
He described the Sept. 11 hijackers as terrorists, a term he rejects when applied to himself and the others involved in the Achille Lauro hijacking.
He said his group was serving a limited, historical goal - the liberation of Palestine - and not the sort of holy war on Americans and Jews declared by bin Laden.
Abbas was a member of the Palestine Liberation Organization's executive committee from 1984 but left in 1991, according to the U.S. State Department.
In 1994, the Achille Lauro caught fire in the Indian Ocean off Somalia and sank.
The U.S. Justice Department has said it has no grounds to seek Abbas' extradition, as there is no outstanding warrant against him. The American warrants were dropped after his conviction in Italy.
A so-called "long-arm" U.S. statute, to aid in prosecution of those committing terrorism against American citizens overseas, was not enacted until after the Achille Lauro hijacking.
In the 1990s, Baghdad, largely out of reach to western security services, had become home to both Abbas and Abu Nidal, another once-feared terrorist mastermind.
Last year, Abu Nidal died violently in Baghdad. Iraqi officials said he committed suicide; Abu Nidal's supporters say the Iraqis killed him.