Italian Prime Minister Bettino Craxi said tonight that the four hijackers of the Italian cruise ship Achille Lauro will be prosecuted in Italy despite U.S. requests that they be extradited to the United States to stand trial for the murder of an American citizen.

Craxi told reporters here that he had persuaded President Reagan early this morning, after sometimes heated discussions between Italian and U.S. officials, that the hijackers must be tried under Italian law.

Several hours later, prosecutors in Genoa, where the cruise began, charged the four men with premeditated murder, kidnaping, hijacking of a ship and possession of arms and explosives, Italian news agencies reported.

Reagan and Craxi spoke around 3 a.m. (10 p.m. EDT Thursday), several hours after four U.S. Navy F14s from the aircraft carrier USS Saratoga intercepted the chartered Egyptair jet bearing the four hijackers over the Mediterranean and forced it to land at the joint U.S.-Italian Sigonella Naval Air Base in Sicily.

The Boeing 737 flew from Sigonella to Rome's Ciampino Airport late tonight with 19 persons aboard, including two Palestinian officials, Egyptian diplomats, security personnel and the crew. One of the Palestinians aboard was identified as Mohammed Abbas, a top leader of the Palestine Liberation Front, of which the hijackers are believed to be members.

In Washington, State Department sources said the United States and Egypt were in sharp disagreement over the disposition of the two Palestinian officials, The Associated Press reported. Egypt wants the two men returned, and U.S. officials are seeking an investigation into whether they played any role in the hijacking.

While officials here did not identify the hijackers, the Italian news agency ANSA identified them as Allah Abdullah Kheshen, 19; Majid Youssef Malaki, 23; Mahmoud Ali Abdullah, 23, and Abdel Latif Ibrahim Fatayer, 20. The four remained in Sicily, and sources said they would be transferred to jail in Syracuse during the night.

According to Craxi, President Reagan personally requested that Italy allow the hijackers to be flown to the United States to stand trial for the murder of Leon Klinghoffer, a 69-year-old retired businessman from New York who, according to reports from the ship, was shot and pushed overboard as the liner sailed off the coast of Syria Tuesday afternoon.

Craxi said that he explained to Reagan that because the killing had taken place aboard an Italian vessel, considered an extension of Italian territory, Italian law dictated that the case be tried in Italy. For a politician to overrule the judicial process, his aides pointed out, would be unconstitutional.

The United States, Craxi said, still would have the right to apply for extradition to the Italian courts, which henceforth will be fully responsible for the prosecution of the four Palestinian hijackers. The four are believed to have boarded the cruise ship at the Italian port of Genoa at the beginning of a 12-day Mediterranean cruise.

Italy, unlike the United States, does not have capital punishment and by law it cannot extradite persons to countries that do. The most the hijackers could be sentenced to in Italy would be life imprisonment.

Craxi explained that the first he had heard of the interception of the hijackers' airliner was at midnight, when Reagan called him to ask his permission for the Egyptian jet and the four U.S. Navy fighter planes to land at Sigonella.

"In consideration of the exceptional situation and heeding the need to pursue the principal end of capturing those responsible for the hijacking and the killing of a passenger," Craxi said at a packed news conference at his offices in the Chigi Palace, "I consented."

After the press conference, Craxi's press secretary, Antonio Ghirelli, termed reports that there had been a coordinated plan by the United States, Italy, Egypt and the PLO as "pure science fiction."

Senior Italian officials said that after the planes landed at the naval air base at about 12:30 a.m. today, there was a conflict over what to do with the hijackers, with U.S. officials seeking to fly them on and Italian officials insisting that they stay. The argument was resolved only after Craxi and Reagan discussed the issue at around 3 a.m.

The diversion of the Egyptair jet has caused new strains between the Italian and Egyptian governments.

Craxi said tonight, before the plane left Sicily for Rome, that as soon as investigations are completed, the Egyptian plane and its crew and, presumably, the two high-ranking PLO officials into whose custody the Egyptians had turned over the hijackers, will be free to fly to Cairo. It was unclear tonight why the Egyptian airliner had been flown to Rome.

Italian officials here said they hoped once the plane was allowed to leave, the Egyptian government would release the Achille Lauro, which has been held in Port Said harbor for similar legal investigations.

Craxi confirmed tonight that one of the PLO members on board was a member of the PLO's central committee and a close aide to Arafat. He identified him as Abbas, the head ot the pro-Arafat splinter faction of the Palestine Liberation Front. Craxi said he could not confirm Israeli reports that the second man was Hani Hassan, one of Arafat's closest advisers.

The Italian prime minister said that Italian authorities were talking to the two senior PLO men because of their instrumental role, along with that of the Egyptians, in negotiating the surrender of the hijackers Wednesday afternoon -- two days after they took over the ship with more than 400 passengers and crew on board after it had sailed out of Alexandria harbor.

As Italian officials stated it, their only interest in the two senior PLO officials was their testimony that could help establish for the Italian courts that the four suspects were in fact the hijackers.

Egypt formally has asked the U.S. and Italian governments to return the two PLO officials who accompanied the four terrorists aboard the intercepted Italian airliner, Washington Post staff writer David B. Ottaway reported.

An Egyptian source in Washington said the request was formally submitted Friday to the State Department and in Rome to the Italian Foreign Ministry.

The source said that Abbas had been instrumental in helping Egypt to persuade the four terrorists to surrender peacefully.

"These are the people who have helped end the whole crisis, and now they find themselves taken," he remarked. "It's not fair."

Italian judicial officials investigating the hijacking in Genoa, where the cruise of the Achille Lauro began Oct. 3, have said they suspect that the hijackers boarded the ship there at the beginning of the cruise with false or stolen passports.

According to the shipping company manifest, two of the men carried Argentine passports (one of which is known to have been stolen in Rome this summer), one had a Canadian passport, and the other had one from Norway.