Italian prosecutors, frustrated by legal delays, began pushing today for a decision on who has jurisdiction in the probe of the hijacking of the Achille Lauro and the slaying of an American passenger.

Genoa Deputy Chief Prosecutor Francesco Meloni said this morning that he was sending a letter to magistrates in Sicily, where a parallel inquiry is under way, to claim the investigation for the Genoa attorney general's office on the ground that the criminal actions began here. Magistrates in Sicily base their claim on the fact that the four suspected hijackers were arrested at a joint U.S.-Italian base near Syracuse.

The magistrates in Genoa say they have reconstructed the killing of the American passenger, Leon Klinghoffer, 69. Genoa investigators said that by piecing together the accounts of the 387 persons aboard the Achille Lauro they had learned that Klinghoffer had been killed after an angry exchange with one of the four hijackers.

[In Rome, an antiterrorism official said Thursday's autopsy had established that Klinghoffer had died of gunshot wounds, The Associated Press reported. He said no bullets were found in the body during the autopsy at Rome's Institute of Legal Medicine.]

The Genoa investigators said their probe into the hijacking, which is now concentrating on the identities of a fifth suspect alleged to have traveled on the ship and other organizers, is being hampered by the unresolved issue of which Italian judicial district is competent to try the case.

Another Genoa magistrate, Luigi Carli, left today for Spoleto in central Italy to question the four suspected hijackers there about the slaying. But in general, Genoa investigators say, they will be unable to take all the necessary steps for their investigation until the question of jurisdiction is settled.

Meloni said this morning that if the Syracuse magistrates insist that they have jurisdiction, the dispute would be referred to the Court of Cassation, Italy's highest court.

This morning a local newspaper, Il Secolo XIX, ran a front-page story saying that Mohammed Abbas, the Palestinian leader whose release from Italy a week ago created a rift with the United States and caused the collapse yesterday of the Italian government, had been seen in Genoa before the hijacking and may be have been the fifth terrorist aboard the ship.

But Meloni denied this, saying, "There is no evidence of Abbas' presence, either in Genoa or on the ship."

Other investigators said magistrates who spent 24 hours aboard the Achille Lauro this week had shown recent pictures of Abbas to passengers and crew members.

"We are sure he was not on the ship," said one investigator.

The investigating magistrates are still trying to identify the man traveling on the ship under the name of Petros Floros who unexpectedly left the cruise, his second or third this year, in Alexandria, Egypt, on the morning of Oct. 7 a few hours before the hijackers took over the ship.

The growing complexity of the case makes it clear that the judicial investigation will be a long one and that a summary trial, possible in Italy only in the first 40 days after a crime has been committed, is unlikely.

Once the jurisdictional dispute is resolved, the local prosecutor's office will have six weeks to decide whether to formalize charges. Once that step is taken, an investigating magistrate will be appointed to the case who will have as long as 18 months for an investigation designed to determine whether the defendants will be tried.

If there is a trial, it could last as long as 18 months. Because of the gravity of the charges likely to be filed against the four Palestinians -- murder, kidnaping, hijacking and illegal possession of arms -- authorities here will be able to keep them in jail throughout the entire investigation and trial.

An extradition request, such as that filed by the United States, first must get approval from the Justice Ministry in Rome. But the final decision rests with magistrates and judges where the case is to be tried.

Prosecutor Meloni said yesterday that granting the American request would be unlikely. Legal conventions between Italy and the United States make it unlawful for both countries to try people for the same crime.

Furthermore, it is illegal here to turn suspects over to a country that has capital punishment unless authorities there promise that there will be no death sentence. Meloni also said that if a criminal is convicted of a crime here and then sent to another country for trial on another charge, he would have to return to Italy to serve his sentence before going to jail elsewhere.