The United States delivered what Italian officials called a "firm and severe" protest today over Italy's refusal to detain a high Palestine Liberation Organization official sought for extradition to the United States, adding to the strains on Italian-American relations following last week's hijacking of the Achille Lauro.

The dispute over Italy's allowing PLO leader Mohammed Abbas to leave the country yesterday, before a U.S. arrest warrant could be served, appeared to set the stage for a major crisis within the five-party coalition government of Prime Minister Bettino Craxi.

U.S. displeasure with Craxi's handling of its request for Abbas' arrest, pending a call for extradition, was expressed today by U.S. Ambassador Maxwell Rabb during a 2 1/2-hour meeting with Italian Foreign Minister Giulio Andreotti. Italian officials later described the protest as "firm and severe."

"Foreign Minister Andreotti and I had a long discussion," Rabb told reporters later. "I pointed out that it is incomprehensible to the government of the United States and to the people of the United States how Abu Abbas his PLO code name could be permitted to leave Italy."

Abbas, the leader of a faction of a PLO splinter group called the Palestine Liberation Front and a member of the PLO's executive committee, was one of two PLO officials brought to Italy with the four hijackers of the Italian liner Achille Lauro after U.S. Navy jets intercepted a chartered Egyptian jet carrying them from Egypt to Tunisia. The identity of the other PLO official is still unknown.

Rabb protested to Andreotti after registering similar complaints yesterday to Prime Minister Craxi.

The four hijackers were arrested Friday by Italian authorities after a showdown between Italian police and U.S. military officials at the joint U.S.-Italian NATO naval air base at Sigonella, Sicily, where the intercepted Egyptian airliner was forced to land.

U.S. officials had hoped to transfer the hijackers -- and apparently the two accompanying PLO officials -- and fly them to the United States, but the Italian government insisted that they should stay in Italy to be tried because the hijacking and the slaying of a U.S. passenger had been carried out on an Italian ship, and thus on Italian territory.

After agreeing with Prime Minister Craxi's arguments that Italian law required the hijackers to be tried in Italy, U.S. District Judge Charles Richey issued an arrest warrant on charges of piracy and hostage-taking against Abbas. Abbas had helped negotiate the hijackers' surrender on an assignment from PLO Chairman Yasser Arafat, who acted at the request of the Italian government.

U.S. officials in Washington argued that Abbas, as leader of the PLF group to which the hijackers allegedly belong, was "criminally implicated in the hijacking of the Achille Lauro and that he planned and controlled the operation."

Italian officials, according to U.S. and Italian sources here, apparently allowed Abbas and the other PLO aide to slip out of the country last night aboard a Yugoslav airliner bound for Belgrade.

Italian Foreign Ministry officials explained today that Abbas had been allowed to leave Italy because Italian officials did not find convincing the U.S. evidence of his alleged complicity in the hijacking.

"The Americans had asked the Italian government to hold Mr. Abbas. We maintain that we made a complete analysis of the request," a Foreign Ministry spokesman said. "Apparently the judgment of the Americans did not coincide with that of the Italian government."

Privately, Italian authorities pointed out that the hijackers have told them the ship's hijacking was an unplanned act, carried out after a waiter walked into their cabin as they were cleaning their guns. Their original intention, they have told Italian officials, was to stage a raid after the ship docked in Ashdod, Israel.

"To maintain now that Abu Abbas, who actually negotiated the hijackers' surrender, was directing the hijacking is simply not something that our evidence bears out," said one Italian judicial official close to the hijacking investigation.

The four hijackers are being held in isolation in a prison in Syracuse, Sicily, Reuter reported. "They are in good condition, they are isolated from other prisoners and their behavior is normal," prison director Carmello Gulli said.

A dispute over the Egyptair Boeing 737 that had carried the hijackers was resolved today when the plane left Rome for Cairo.

The controversy over Abbas' flight from Italy, however, not only has roiled U.S.-Italian relations but also has strained the coalition that has allowed Craxi, a Socialist, to rule Italy since 1983.

Craxi and Foreign Minister Andreotti, a Christian Democrat, have adopted a strongly pro-Arab foreign policy that has not had the enthusiastic support of their coalition partners. Republican leader Giovanni Spadolini, who is also minister of defense, was openly critical of the government's request to Arafat to help negotiate an end to the hijacking. Craxi has called a special Cabinet session for Monday to debate the issue.