JIDDAH, SAUDI ARABIA, SEPT. 15 -- Saudi Arabia and the Soviet Union are set to reestablish diplomatic relations next week after a 52-year suspension caused largely by Soviet leader Joseph Stalin's refusal to allow his Moslem population to make pilgrimages to Mecca.

The Saudi foreign minister, Prince Saud Faisal, was on his way to Moscow today to make the formal announcement jointly with Soviet Foreign Minister Eduard Shevardnadze in a ceremony that Saudi sources here said was expected to take place Wednesday.

The United States, which for years exercised its influence to prevent the kingdom from establishing diplomatic relations with Moscow, has raised no objection to it, giving another sign of the changes in U.S.-Soviet relationships brought about by the waning of their Cold War rivalry.

Significantly, also present for the ceremony in Moscow will be the Saudi pilgrimage affairs minister, Abdul-Wahab Abdul-Wasie, who is already in Moscow for negotiations on the issue that helped cause the so-called suspension in Saudi-Soviet relations in 1938.

The Soviets have agreed to allow 1,000 or more Moslems to make the annual pilgrimage, or hajj, to Mecca, Islam's holiest city, next June. The two nations reached an earlier agreement to allow Saudi Arabia to ship 1 million copies of the Koran to the Soviet Union.

The pilgrimage is one of five sacred duties every Moslem is called upon to make during his or her lifetime.

The Saudi government has deliberately involved the kingdom's ultra-conservative Islamic leaders in almost two years of negotiations with Moscow to help make any agreement to restore relations palatable to the kingdom's religious establishment.

The Soviet Union and Saudi Arabia never formally broke diplomatic relations, which date back indirectly to the presence of a Soviet diplomatic mission in the Hijaz, the kingdom's western province where the holy cities of Mecca and Medina are located, when it was under the independent rule of the Hashemites in the early 20th century. Saudi Arabia's ruling Saud family conquered the Hijaz and made it part of the kingdom in 1923-24.

The Soviet diplomatic presence continued until 1938 when Stalin recalled his ambassador after a dispute with the Saudi government over his refusal to allow Soviet Moslems to travel to Mecca for the hajj.

U.S. sources said the timing of the resumption of diplomatic relations was partly explained by the Saudis' desire to establish a closer working relationship with Moscow during the current crisis over Iraq's annexation of Kuwait and to consolidate Soviet support for various U.N. resolutions aimed at forcing an Iraqi withdrawal.

But they said it probably would have happened soon in any case because of a growing number of shared concerns -- notably oil and conflicts with Iran and Iraq -- that had arisen over the past two years.