Prime minister designate Bettino Craxi today succeeded in reconstituting the same five-party coalition government that collapsed two weeks ago in the wake of the Achille Lauro affair.

After meeting for three hours this morning with leaders of the five parties that had formed his government, Craxi announced to journalists, "The crisis has been overcome."

Craxi confirmed that the agreement entailed using a rare constitutional formula under which, in effect, he would withdraw his resignation of Oct. 17 and submit his original government to a parliamentary vote of confidence next week. A positive result of the vote already has been assured in the negotiations with party leaders.

The resolution of the crisis, brought about by disagreements within the coalition over the government's handling of the hijacking of the Italian cruise ship Achille Lauro and its aftermath, came as Italy's Court of Cassation ruled that the investigation into the hijacking and the prosecution of the ship's four hijackers would be handled by prosecutors in Genoa, the ship's port of departure.

In assigning the case to Genoa, the Italian court said that it would let stand an arrest warrant issued by the deputy prosecutor in Syracuse, Sicily, last weekend against Mohammed Abbas, the Palestinian official who the U.S. government contends masterminded the hijacking that resulted in the death of an elderly, invalid U.S. citizen.

The United States had demanded that the Italians arrest Abbas pending a U.S. request for his extradition, but Craxi has insisted that the United States failed at the time to provide enough evidence under Italian law for Abbas to be arrested. He has said since that whether Abbas ultimately was proven to be the leader of the hijackers did not detract from the fact that sufficient evidence was not provided immediately after Abbas landed in Italy.

The Syracuse prosecutor had been conducting a rival investigation to the one in Genoa because the four hijackers, Abbas and one of his aides had been brought to Italy in an Egyptian airliner that was forced to land at the U.S.-Italian naval air station at Sigonella, in Syracuse's jurisdiction.

Court officials said that the transfer to Genoa of all judicial responsibility for the hijacking investigation would not prevent a parallel court investigation begun this weekend by Syracuse's deputy state prosecutor, Dolcino Favi, into the tense confrontation that occured at Sigonella between Italian carabinieri and U.S. Delta Force commandos after the Egyptian plane bearing the hijackers was forced to land there.

Favi launched his investigation into what the Italian press has dubbed the "hot night" at Sigonella to see if any Italian laws had been broken by U.S. military officials at the Italian base when the Delta Force commandos sought to capture the hijackers and Abbas to fly them to the United States for trial.

A cordon of 50 carabinieri reinforced by Italian military policemen surrounding the Egyptian plane kept the U.S. troops from carrying out their mission. In the end, President Reagan ordered the U.S. troops to stand down after Craxi explained to him that Italian law demanded that the hijackers be tried in Italy because their crimes had been committed on an Italian ship.

Craxi's subsequent decision to allow Abbas to leave Italy despite U.S. demands that he be arrested and held for extradition led the pro-American leader of the Republican Party, Defense Minister Giovanni Spadolini, to pull his party's three ministers out of the coalition in protest, and the government collapsed.

Spadolini apparently was persuaded to rejoin the government today when Craxi agreed to his demands that there be more consultation within the governing coalition in the future and restated Italy's commitment to oppose international terrorism and stand by its Atlantic Alliance partners, especially the United States.

As part of their compromise, the parties agreed to toughen their stance toward the PLO. Apparently reflecting Spadolini's demands, the parties declared that the PLO should be allowed to take part in Middle East peace negotiations only if it "follows without reservations the road of peaceful negotiations."

Spadolini today said that there were no "victors and no losers" as a result of the crisis. But Italian political commentators said that the Republican-sparked government crisis had left the party dangerously isolated, threatened new parliamentary elections and endangered pending financial and government reforms dear to the party, thus leaving Spadolini no choice but to rejoin the coalition after a face-saving agreement was reached.

Craxi said that once the leaderships of the various coalition parties approved the decision to resume the government reached by their party secretaries, he would go to see President Francesco Cossiga and withdraw his resignation. That would open the door for Craxi to put his continuation as prime minister to a vote of confidence in Parliament next week.

The formula for returning to power was in fact urged on Craxi by Cossiga during the weekend as a means of speeding up the formation of a new government so it could get on with the pending financial legislation.