A week ago, the U.S. interception of the Egyptian airliner carrying the four Palestinian hijackers of the Achille Lauro cruise ship appeared to be a stunning success for the United States in its war on international terrorism.

But if the military maneuver was a triumph, its diplomatic consequences have proven less than triumphal. The 26-month-old Italian government, one of America's most loyal friends in Europe, has fallen. Egypt, a linchpin of U.S. diplomacy in the Middle East and second-largest recipient of U.S. aid, is furious at the United States, and its moderate government has been shaken. U.S. relations with its other moderate Arab allies have been seriously strained.

Various Egyptian and Italian sources have been warning here in recent days that unless the Reagan administration does something quickly to repair relations with Cairo and Rome, the interception could have serious destabilizing effects inside both countries, and could compromise the remaining thin hopes for reviving the whole Mideast peace process. For days after the incident, the administration continued to lambast its allies, particularly the Italians, whom Attorney General Edwin Meese III and White House spokesman Larry Speakes denounced again Wednesday for releasing Mohammed Abbas. Abbas is the Palestinian who -- at Egyptian and Italian behest -- persuaded the Achille Lauro hijackers to surrender, then accompanied them out of Egypt.

Ironically, an Italian source noted, had Italy turned Abbas over to the United States, there could have been "an explosion" in Egypt's relations with Italy and the United States.

Now at stake, according to these sources, is the future survival of the pro-American Egyptian government of President Hosni Mubarak and its ability to maintain its close alliance with Washington or even its "cold peace" with Israel.

One Italian source said that unless the Reagan administration acted more forcefully to smooth over its differences with Italy, it could prove impossible to reassemble the five-party coalition that has given Italy one of the longest-lived governments in its politically unsettled post-World War II history.

"The administration has got to say something to help us," he pleaded.

A private Egyptian emissary visiting here said that the humiliation dealt to Egypt's national pride by the U.S. interception of the Egyptian plane had stirred opposition as never before to the Mubarak government among the Islamic fundamentalists and even set off "rumblings" in the armed forces there. "Very frankly, there has to be action by the United States in order to get us out of this Archille Lauro mess," he said. Mubarak, he remarked, "has been feeling the crunch" since his pro-American foreign policy "has not reaped any harvest as yet" and he is now fighting the fundamentalists "very hard."

"If things mushroom in Egypt, where would you be?" he added.

Both these emissaries pointed out that the United States was in the process of undermining two of its very closest allies, one a pillar of the NATO alliance and the other the only Arab country to have made peace with Israel. The two countries, they noted, were previously cooperating closely with Washington in intelligence and military matters as well as in supporting its East-West and Mideast policy goals.

Italy has accepted without hesitation the deployment of U.S. cruise missiles over stiff objections from the Soviet Union, participated in the U.S.-led peacekeeping forces that went to Beirut in 1982, and delivered into U.S. hands the high-ranking KGB official, Vitaly Yurchenko, who defected to the West last July.

Egypt has just finished carrying out joint military maneuvers with the United States, provides the United States with a secret air base on a contingency basis for its Mideast military operations.

The Egyptians have also noted that while the Reagan administration was striking out rhetorically at Cairo -- supposedly a close friend, and one that had just saved the lives of hundreds of passengers and crew on the Achille Lauro -- it was praising Syria, the main foe of U.S. efforts to make peace in the Mideast.

Syria, Egyptians note, was warmly thanked for refusing to allow the Achille Lauro to put in at any Syrian port and for turning over the body of the dead U.S. hostage, Leon Klinghoffer. "People are saying it doesn't pay to be friendly to the United States," one Egyptian said. "Syria got all the pats for its help."