Abbas is the admitted mastermind of the hijacking of the Italian cruise ship Achille Lauro in 1985, but has always insisted that the murder of passenger Leon Klinghoffer -- an American tourist -- wasn't his fault.
Saddam Hussein gave Abbas sanctuary. The Italians have sentenced him to life in prison. Wednesday, the Palestine Liberation Organization called for his release. But the U.S. says it's studying its own murder charges and is not about to release him.
"Abu Abbas is a terrorist. He was a terrorist. He remains a terrorist and he will be viewed as such," said Brig. Gen. Vincent Brooks.
Meanwhile, CBS News Correspondent Jim Stewart reports U.S. forces have more names on their terrorist shopping list now that Baghdad has fallen.
Next up may be Abdul Yasin, accused of helping make the bomb in the first World Trade Center attack in 1993. Yasin also fled to Baghdad but was greeted with suspicion and put in jail. He's even showed reporters the scars he got while mixing the bomb.
Most intriguing is Ahmad Khlil Al-Ani. He worked at the now ransacked headquarters of Iraqi Intelligence. But he was once stationed in Prague. There are conflicting reports about whether he secretly met 9-11 hijacker ringleader Mohammed Atta there in April 2001. If so, what did they discuss?
Also missing is Abu Zaqawi, an al Qaeda lieutenant who lost a leg fighting in Afghanistan and got treatment in Baghdad. And there's Farouk Hijazi an Iraqi ambassador tied to a 1993 assassination attempt against former President George H.W. Bush. Hijazi may have escaped to Syria by now.
Some of these men may have suspected a day of reckoning would come. Abu Abbas, for one, told a visiting American journalist last year that, after thinking it over, he'd decided that killing civilians is wrong.