The Pentagon said on Tuesday that Abbas, 55, died of apparent natural causes the previous day.
He had been held by the occupation military in Iraq since his arrest there on 14 April.
"Initial reports indicate that he apparently died of natural causes. Medical efforts to revive him were unsuccessful. An autopsy will be performed," Bryan Whitman, a US Defence Department spokesman, said.
Family 'denied justice'
Whitman refused to say where Abbas had died. However, another defence official, who asked not to be identified, said he was being held in Iraq at the time of his death.
The family of Leon Klinghoffer, the sole victim of the 1985 Achille Lauro hijacking, said they had been denied justice by his death.
"The one consolation for us is that Abu Abbas died in captivity, not as a free man," Klinghoffers' daughters Ilsa and Lisa said in a statement.
Klinghoffer, an American Jew, was shot in his wheelchair and thrown overboard after Palestinian hijackers, led by Abbas, took over the ship on which he had been spending a wedding anniversary cruise with his wife. He was 69.
"The one consolation for us is that Abu Abbas died in captivity, not as a free man"
Ilsa and Lisa Klinghoffer
The Klinghoffer family spent 18 years seeking Abbas's capture and eventual extradition to the United States to stand trial.
"Abu Abbas was a vicious terrorist who was responsible for countless deaths of innocent people - men, women and children - throughout the Middle East," the family statement said.
"His trial and conviction also would have sent a clear message to terrorists everywhere that, if they kill an American citizen, they can run but they can't hide."
Abbas was sentenced in absentia in Italy to five life terms for his role in the Achille Lauro hijacking.
He said he took over the cruise liner to draw the world's attention to Israeli persecution of the Palestinians.