Reagan administration officials said last night they would ask the Italian government for "prompt extradition" of the four hijackers of the Achille Lauro cruise ship, and the head of the Justice Department's Criminal Division said he was "supremely confident" the United States can prosecute them.

"It is our desire they be brought to justice," White House spokesman Larry Speakes said. "It is our intention to ask for extradition."

But Speakes said there was no prior agreement with the Italian government to send the hijackers to the United States and said the matter would have to proceed "through the Italian justice system."

Assistant Attorney General Stephen S. Trott said that under existing U.S. laws, "We do have long-arm jurisdiction over hostage-taking of Americans abroad. We do have jurisdiction that extends way beyond the territories of the United States that's been carefully spelled out by Congress."

However, a former State Department attorney who specialized in international affairs said last night that he thought it would be extremely difficult to prosecute the hijackers under U.S. law.

"Ordinarily, a murder of an American outside the United States is not a violation of U.S. law," the official said. "I'm not sure what these people could be prosecuted for. It's a mystery to me."

Trott said a "team of experts" in the Criminal Division had discussed the issue yesterday and had assured him that the legality of prosecuting the hijackers "isn't ambiguous at all," even though the hostage-taking and the killing of American Leon Klinghoffer took place on an Italian cruise ship in international waters.

He said that preparations for prosecuting international terrorists have been a high priority under Attorney General Edwin Meese III. "We have a group of people in the Criminal Division who are very much up to speed on this," he said.

Trott noted that a group of Colombians who attacked Drug Enforcement Administration agents in Colombia had been prosecuted successfully in Florida in recent years. "The constitutionality was litigated and upheld," he said. "The principle is a valid principle. We're supremely confident it would be upheld."

Congress made this authority even more explicit in passing the 1984 Comprehensive Crime Control Act, Trott added.

The 1984 act requires imprisonment for "up to life for taking hostages" either in this country or abroad in an effort to force a government or third party to take a particular action, such as freeing other prisoners. But, according to a Congressional Quarterly analysis of the act, it also bars prosecution under the terrorism section "unless the offender or person detained was a U.S. national, the offender was found in the United States or the U.S. government was the one the offender sought to influence."

The former State Department lawyer also said it was not clear that U.S. law covered the hijacking of a foreign ship.

Trott emphasized that he was not commenting on any specific legal case that might result from the hijacking of the Italian cruise ship.