Behind the public pomp and oratory of his world tour, President Carter was warned by leaders in Western Europe and the Persian Gulf that the United States must apply "countervailing pressure" to deepening Soviet intrusion in Ethiopia or risk signaling that the anti-Communist world in the end may lose by default.

That warning came from the shah of Iran, the president of France and the king of Saudi Arabia. It points up one strong lesson of the first Carter year: Three years after Vietnam, the United States must assert its full role in the real world of international politics or lose the confidence of its friends and allies.

Carter was urged both in Europe and in Iran and Saudi Arabia to put the strategic arms limitation talks in mothballs indefinitely to compel Moscow to halt military operations in Ethiopia. One European leader told the Carter traveling party: "Detente is not a sausage to be cut in a Soviet pattern, but a continuous process everywhere."

The huge Soviet airlift to Ethiopia started in late November. Without revealing the reason, Carter sent Under Secretary of State Philip Habib to Moscow in early December, ostensibly to explain the U.S. position on Israeli-Egyptian negotiations but actually to protest the Kremlin's Ethiopian adventure.

Habib protested the Soviet airlift to the horn of Africa, the strategically important land shared by Ethiopia and Somalia that juts into the Indian Ocean at the entrance of the Red Sea. Habib's catch in Moscow: exactly nothing.

So 225 large Soviet Antonov cargo planes continue to ferry supplies to Ethiopia, violating the air space of half a dozen sovereign states and piling up military supplies far in excess of Ethiopia's conceivable needs. That newly Marxist state, assisted by perhaps 3,000 Soviet and Cuban military advisers, is fighting a war against Somalia that could decide the future of eastern Africa and ultimately control of the Persian Gulf oil riches.

The angry reaction from non-Communist states came early in the Carter trip. In Tehran, the shah said flatly that his country would "react" if the Soviet-backed Ethiopians set one foot across the border of Somalia. Presumably this would mean an Iranian airlift (or sealift from Saudi Arabian bases across the Red Sea) to bolster Somali forces. Ever since Somalia expelled the Russians last year, it has sought U.S. aid - in vain.

In Paris French President Valery Giscard d'Estaing revealed his decision to press hard for the Organization of African Unity, led by non-Marxist French-speaking states, to warn Mascow that Africa is off bounds. Carter agreed to help. Soon afterward, Giscard went to the French-speaking Ivory Coast to start organizing a massive continent-wide campaign for maximum political pressure against the Soviet Union.

In Saudi Arabia, the agitation of King Khalid was even more intense. Thus, during the trip, Carter agreed to persuade Somalia to seek a cease-fire in the war with Ethiopia. The United States would then put heavy pressure on Moscow to compel Ethiopia to accept that offer. Next would come a demand led by major African states - Egypt, Sudan and possibly Kenya - for Soviet withdrawal from Ethiopia.

If the Soviets stonewalled this international effort as Habib was stonewalled in Moscow last month, President Carter would come under heavy pressure from Iran, Saudi Arabia and U.S. allies in Europe to use SALT II as a lever against Moscow.

Manly hard problems are posed by the European-Iranian-Saudi plan to put a stop to free-wheeling Soviet intervention in Ethiopia. The shah, despite heavy investment in American arms, cannot legally permit their use by a third country. The same is true of Saudi Arabia, so fearful of rising Soviet involvement across the Red Sea that it now keeps at least two divisions on its southern Red Sea coast.

That raises this question: Would Congress give these U.S. allies a waiver to ship their U.S. arms to Somalia? Some experts here fear the answer would be no. Nor is there any slight indication that Carter would endanger his oft-repeated pledge for a SALT II agreement by employing the arms talks as a political lever.

These caveats aside, Carter came home with a loud and clear message from this nation's most formidable friends. Whether that message struck home, as some of these nations believe, will not be known for several weeks. What is clear now is that without U.S. leadership, the pressures on the horn of Africa and everywhere else will continue in one direction. For thenon-Communist world, that direction is down.