The government of Prime Minister Bettino Craxi today faced imminent collapse after one of the five parties in the coalition withdrew in protest over the government's handling of the hijacking of the cruise ship Achille Lauro.

The fall of Craxi's 26-month-old government, one of the longest-lived in postwar Italy, became a virtual certainty today when the tiny but influential pro-American Republican Party of Defense Minister Giovanni Spadolini announced that it was quitting Craxi's governing coalition because it had not been adequately consulted during the hijacking crisis and its aftermath.

Sources close to President Francesco Cossiga said tonight that Craxi was expected to visit the president Thursday morning and formally present his resignation, thus avoiding a parliamentary debate on the Craxi government's foreign policy.

The planned debate had been considered an explosive potential for fragmenting the governing consensus that has prevailed in Italy since Craxi took over the prime ministership in August 1983 to head Italy's 44th government since the end of World War II.

As the man with the greatest chance to put together another government, Craxi is expected to be charged by Cossiga with trying to form a new coalition, most probably with the four remaining parties that have, with varying degrees of enthusiasm, supported him during the hijacking crisis. Aside from the Republicans and his own Socialist Party, Craxi's government had been supported by the dominant Christian Democrats, the Liberals and the Social Democrats.

The collapse of Craxi's government just one month short of becoming the longest-serving government in postwar Italy came after unprecedented U.S. criticism of Craxi's handling of a Washington request for the extradition of a senior Palestinian official, Mohammed Abbas. U.S. authorities accuse Abbas of masterminding the Achille Lauro hijacking, which resulted in the death of Leon Klinghoffer, a 69-year-old passenger.

From the moment that the Achille Lauro was hijacked by four young Palestinians off the coast of Egypt during a Mediterranean cruise, there had been tension over the government's handling of the affair, with Craxi and Foreign Minister Giulio Andreotti on one side and Spadolini on the other.

Craxi and Andreotti, who only a week earlier had vehemently criticized the Israeli bombing of the headquarters of the Palestine Liberation Organization in Tunisia, particularly had angered Spadolini by asking for help in ending the hijacking crisis from PLO Chairman Yasser Arafat.

Spadolini, a supporter of Israel who consistently has criticized the government's pro-Arab foreign policy, denounced the government's request for help from Arafat. He did not accept the assignment by Arafat of Abbas, the leader of the faction of the Palestine Liberation Front to which the hijackers apparently belong, to conduct the negotiations for the hijackers' surrender.

When Abbas, an aide and the four hijackers were forced to land in Sicily after U.S. Navy F14 jets intercepted the chartered Egyptian airliner that had sought to transport them from Cairo to Tunis, Spadolini supported U.S. demands for Abbas' arrest.

Craxi and Andreotti have argued that Abbas was protected under diplomatic immunity while in Italy by virtue of an Iraqi diplomatic passport that he carried and because the Egyptian airliner he was on also was protected by diplomatic immunity.

Craxi furthermore has denied that the United States provided Italy with conclusive evidence of Abbas' alleged leadership of the hijacking and maintained that the Italian courts had found no reason to arrest Abbas on the basis of the information supplied by Washington.

The final straw, however, was the decision by Craxi and Andreotti to allow Abbas to leave Italy Saturday despite U.S. requests for his arrest. Spadolini, who was out of Rome Saturday, complained bitterly that Abbas should not have been allowed to leave Italy for Yugoslavia without his being consulted.

Maurizio Cremasco of the Italian Institute for International Affairs said today in an interview that part of the reason Spadolini bolted the government was that he was "trying to be more American than President Reagan." He said that the crisis was one of the unfortunate fallouts of President Reagan's unprecedented decision to force down the Egyptian plane carrying the hijackers.

Magistrates said yesterday that they had issued arrest warrants for three persons in addition to the four Palestinians already charged in the hijacking affair.

One of the three, who has given his name as Kalaf Mohammed Zainab, was detained in Genoa Sept. 28 for holding two false passports, and magistrates revealed Monday that he had now also been charged in the Achille Lauro hijacking. Officials said the other two were a man who bought the ship tickets for the hijackers and a man who is believed to have been part of the commando unit but who disembarked at Alexandria before the vessel was seized Oct. 7.