Palestinian militant Abu Abbas, captured this week in Baghdad, does not have immunity under a peace accord between Israel and the Palestinians, the US says.
Abbas has been based in Iraq for the past 17 years
Abbas masterminded the hijacking of the Italian cruise ship Achille Lauro in 1985 and was sentenced in absentia to five life terms by an Italian court.
Italy says it will seek his extradition.
The Palestinian Authority has called for his immediate release, citing 1995 peace accords that include an amnesty for Palestine Liberation Organisation (PLO) officials.
However, a US State Department official said on Wednesday the clause dealt only with the detention and prosecution of certain people in the jurisdiction of Israel and the Palestinian Authority.
We want to know that he will serve his full sentence - which is hopefully a life sentence
daughter of executed hostage
"It does not apply to the legal status of persons detained in a third country," the official said.
The daughters of an elderly American Jewish tourist killed during the hijacking of the Achille Lauro have called for Abbas to be tried in the US.
Leon Klinghoffer, who was confined to a wheelchair, was shot dead and his body flung into the sea.
"We want [Abbas] brought here," Lisa Klinghoffer told NBC news, speaking for herself and her sister Ilsa.
"We want him tried here in our country. We want to know that he will serve his full sentence - which is hopefully a life sentence."
Italian Justice Minister Roberto Castelli said his government had asked Egypt and Jordan in the past few months for Abbas' extradition when it believed he was in those countries.
He said his department was now working to untie the "legal knot" of where it should send its extradition request, given that he was being held by the American authorities.
Leon Klinghoffer was killed during the hijacking of the Achille Lauro
US officials had earlier said it was not clear whether Abbas would be extradited for trial, saying only that "justice would be served".
The US sees the capture of Abbas as proof that Saddam Hussein's regime supported terrorism.
"He was a terrorist and he remains a terrorist," Brigadier-General Vincent Brooks, a US military spokesman at Central Command in Qatar, said on Wednesday.
"More importantly, he was found in Baghdad and we've said
for a long time that Baghdad and the Iraqi regime that no longer
exists have harboured terrorists."
Abbas and the group he led, a faction of the Palestine Liberation Front (PLF), have been based in Iraq for the past 17 years.
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The PLF called for the immediate release of its leader on Wednesday.
"We consider the US-British coalition responsible for the safety
of our secretary general and we demand that he be released
immediately," it said in a statement received by AFP news agency in Beirut.
Palestinian officials say Abbas should not have been detained.
Abbas still inspires strong loyalties
Cabinet minister Saeb Erekat called on Washington to respect the 1995 peace deal - signed by then President Bill Clinton - which specified that PLO members could not be tried for acts of violence committed before 1993.
Under the deal, Israel's Supreme Court in 1998 declared Abbas immune from prosecution in Israel over the Achille Lauro hijacking.
Abbas had visited the West Bank and Gaza many times in co-ordination with the Americans and the Israelis, Mr Erekat said.
The PLF carried out the 1985 attack on the Achille Lauro in an attempt to secure the release of 50 Palestinian prisoners being held in Israel.
The ship was seized while sailing between the Egyptian cities of Alexandria and Port Said.
After a two-day stand-off, Egypt gave free passage to the hijackers in exchange for the rest of the hostages - many of them Americans.
But the plane carrying the hijackers to Tunisia was intercepted by US navy jets and forced to land in Italy.
Abbas' co-conspirators were sentenced to long prison terms but he was freed by the Italian authorities who said they had insufficient evidence to detain him.
However, he was later convicted in absentia of masterminding the hijacking.
In 1996, he apologised for Mr Klinghoffer's death, describing the killing as a mistake.