The Reagan administration reacted with caution yesterday to the seizure by Palestinian terrorists of an Italian cruise ship, saying only that the United States had contacted other governments involved to discuss what "appropriate action" might be taken to end the drama.

The Italian and U.S. goverments urged Syria to not allow the ship to dock at any of its ports following reports that it was heading for the southern Syrian port of Tartus, according to U.S. officials. Both governments were understood to be particularly anxious that it not be permitted to put in at Beirut to prevent a repetition of the TWA hijacking crisis of last June, when 39 Americans were held hostage for 17 days by Shiite captors.

President Reagan, speaking during a picture-taking session with Singapore Prime Minister Lee Kuan Yew, refrained from commenting in detail, saying only that he thought it was "the most ridiculous thing."

"I think all governments, and particularly those who have passengers on that ship, from more than a dozen countries, are vitally interested," he added.

In contrast to past administration behavior in similar crises, Reagan and other top officials appeared to go out of their way to avoid comments that could be interpreted as confrontational. Officials indicated the administration was content, at least initially, to let the Italian government take the lead in deciding how to deal with the terrorists.

An interagency U.S. task force was established to handle the crisis round the clock, while Reagan and his senior aides were reported to be following developments closely.

The White House also refused comment on U.S. military operations in the Mediterranean. NATO naval exercises, involving U.S., British and Italian warships, have been under way since before the Achille Lauro was seized on Monday.

The Defense Department did confirm, however, that the guided missile destroyer USS Scott cut short its port visit to Haifa and steamed into the eastern Mediterranean to be available if needed. The conventionally powered aircraft carrier USS Saratoga was steaming westward in the Ionian Sea between Italy and Greece with other warships involved in the NATO exercise.

"It's wait and see around here now," said one Pentagon official. "We're waiting to see what the Italians do. They have some good antiterrorist teams."

White House and State Department officials stressed that there was no change in the U.S. policy of refusing to negotiate with terrorists or pressuring other governments to do so.

White House spokesman Larry Speakes, in response to questions, drew a distinction between the possibility of "discussions" with those commandeering the Italian liner, which he said was permissible, and "negotiations," which he excluded under U.S. policy.

Discussing the U.S. role, Speakes said Washington would seek to coordinate with other governments affected by the hijacking. But he added the White House did not believe any single government should be assigned the task of dealing with the terrorists.

Pentagon officials, like those in other government agencies, were under orders to remain tight-lipped about ship movements and contingency planning. By contrast, the administration was much more strident and open about military movements during the hijacking last June of a TWA airliner to Beirut.

The Delta antiterrorist team stationed at Fort Bragg, N.C., was activated during that TWA crisis but did not go into action. The Pentagon never confirmed that the unit had been activated then, and last night refused to discuss the possibility of Delta troops being flown to a Middle Eastern base for this crisis. One administration official would only say, "We will do what is necessary to protect our citizens."

White House and State Department officials said the exact number of Americans among the more than 420 hostages aboard the Achille Lauro was not known, but said that their best estimate was that "perhaps a dozen" were still aboard.

They had no confirmation of reports that the terrorists, identified as belonging to the tiny Palestinian splinter group, the Palestine Liberation Front, had shot one American hostage on the ship.

Most of the 70 to 80 American tourists who boarded the ship in Genoa, Italy, had disembarked in Alexandria for a sightseeing tour of Cairo and were safe there, the officials said.

Speakes and national security affairs adviser Robert C. McFarlane not only declined comment on possible U.S. actions but they also remained silent on the U.S. attitude in general toward the hijacking.

The Achille Lauro piracy is believed to be the most serious terrorist incident at sea since the seizure of the luxury liner Santa Maria with 600 aboard by Portuguese dissidents in 1961.

Officials said that within hours of learning of the incident between 5:30 and 6 p.m. Monday afternoon, the administration had set up an interagency task force under Secretary of State George P. Shultz to follow the situation.

Throughout Monday night, the State Department had "a considerable amount" of communications with U.S. embassies in Rome, Tel Aviv, Cairo and Damascus as well as "appropriate governments" in the region, Speakes said. Those governments were later identified by U.S. officials as Egypt, Israel, Syria and Tunisia.

Pentagon officials said U.S. warships could be ordered to shadow the Italian cruiser, but remarked that any use of their guns could put the hostages at high risk.