DHAHRAN, SAUDI ARABIA, OCT. 31 -- Behind the Soviet Union's growing role in the Persian Gulf crisis are some hard-headed calculations about Moscow's economic and diplomatic interests, according to U.S. and Saudi officials.

One quick payoff is Moscow's budding business relationship with oil-rich Saudi Arabia. Moscow's top foreign trade official led a mission here last week to promote expanded bilateral trade, tourism and investment, the first Soviet cabinet-level visit to Saudi Arabia since diplomatic ties were restored in September.

The other main thrust of Soviet policy, which has become clear over the past week, is to position Moscow as a Middle East peacemaker. Soviet President Mikhail Gorbachev pushed for a diplomatic settlement of the crisis last weekend during his visit to France, claiming that "some signs are emerging that Iraq's leadership may be heeding the will of the United Nations."

U.S. officials were dubious about Gorbachev's claim, and one senior official in Washington said he was skeptical about how much the Soviets were helping the American campaign to force Saddam to withdraw unconditionally from Kuwait.

A clear U.S. "victory" in the gulf crisis would not serve Soviet interests, the senior American official noted, saying it was apparent Moscow wanted the Americans out of the gulf after the crisis is settled. He said that recent moves by the Soviets should be seen as calculated efforts to distance themselves from any negative fallout in the Arab world should the gulf crisis lead to war and to protect Soviet interests in a region of the world that is important to them strategically.

The Soviet economic opening with Saudi Arabia may offer some quick benefits. In his meetings last week with Saudi businessmen and officials, visiting Foreign Trade Minister Konstantin Katochev negotiated an agreement on more favorable trade terms. He also said Soviets were interested in investing in Saudi high-technology defense and oil ventures, and said trade costs would go down because "middlemen" could be eliminated.

But as he left Sunday, Katochev mentioned that the gulf crisis was costing the Soviet economy between $8 billion and $10 billion. According to some Saudi officials and Western analysts, this may be the biggest motive for Moscow's recent high-profile effort, led by Arab specialist Yevgeny Primakov, to find a peaceful resolution to the continuing crisis.

"They are absolutely beside themselves with concern about both the direct and indirect effects on their economy," said Karen Dawisha, a Soviet policy expert from the University of Maryland. And it comes at a time when the Soviets already are extremely worried that "the West will go by itself into a major recession," resulting in "zero chance of economic aid to the Soviet Union," she added.

A senior Saudi official agreed. The Soviet role in the gulf crisis set off by Iraq's invasion of Kuwait Aug. 2 "has been indispensable, extremely positive," he said. But the Soviets' main concern, he added, is "their economy. They want to solve their problems in Moscow and Leningrad. . . . They don't care about what's happening outside."

"They are very much interested now not to allow anything to interfere with the possibility of economic {assistance} from America, Europe, Japan and the gulf countries," he said. "If these countries are either too busy to help or their economies have been affected because of the crisis, they feel that they are directly being affected."

The official indicated that Saudi Arabia was ready to give Moscow aid, and cited Katochev's visit as a start in that direction. Katochev, who was received by King Fahd, is believed to have raised economic aid in his private discussions with Saudi officials, but the outcome of those talks is not known.

Something the Saudis hoped to bring up in the bilateral talks, a Saudi official said, was the purchase of military transport vehicles, which the Soviets have in bulk and the Saudis need for the Arab forces that have joined the multinational military buildup in their country. "With this crisis we need so many little things -- we need jeeps, trucks, water tanks."

It is not known whether such a deal was struck, but the Soviets have been reluctant to do anything that suggests they are contributing to the U.S.-led military buildup, one Saudi source said. For example, the Soviets declined to transport additional Syrian troops here, a decision interpreted by the Saudis as an effort by the Soviets to distance themselves from the military deployment.

Katochev's visit illustrated the expanded diplomatic and economic opportunies for the Soviet Union in the Middle East created by the renewal of ties with Riyadh, which were suspended in 1938 after Joseph Stalin refused to let Soviet Moslems make the hajj, or pilgrimage, to Mecca. For the Soviets, the new ties mean direct, open access to the wealthiest Arab state, and the most important one in the Arabian peninsula.

"We had some trade and economic ties even before," said Sergei Peskov, first secretary at the Soviet Embassy in the nearby United Arab Emirates. "I think we can expect a boost -- well not a boost, but normal development of these ties in the future." Politically, Peskov said, "it can only lead to stabilizing the Middle East in the future."

Saudi Arabia was the last Arab state to normalize its relations with Moscow in the wake of the foreign policy changes brought about by Gorbachev.

In the Cold War years of superpower competition, the Soviet Union had concentrated on building up its military ties with key Arab states such as Egypt, Syria and Iraq. Staunchly anti-communist and firmly in the American camp, Saudi Arabia long saw the Soviet Union's atheistic philosophy as anathema to Riyadh's strong Islamic religious principles.

But with the changes under Gorbachev and his pullout from Afghanistan, where Saudi Arabia supported Moslem guerrillas fighting the Soviet-supported Marxist regime, the barriers to renewed ties fell away.

Although the two countries had been talking of restoring ties for almost two years, the gulf crisis prompted a speedy renewal as the Saudis sought to forge an international coalition to isolate Iraqi President Saddam Hussein at the United Nations.

Khaled Maeena, editor of Arab News, said the gulf crisis simply "oiled the wheels" for the resumption of ties, which the Soviets "felt was overdue" and which was already in the cards because of the changing nature of Soviet society. Those changes are said to have impressed King Fahd, who, according to one source, has privately called Gorbachev "one of the geniuses" of this century.

Even before ties were restored, the Soviets had permitted Saudi Arabia to ship a million copies of Islam's holy book, the Koran, to Moslems in the Soviet Union. Moscow also has agreed to allow at least 1,000 Soviet Moslems to make the hajj next year.

This glasnost, as Gorbachev's policy of openness is called, is apparently working both ways. A few months ago, an Arabic translation of Gorbachev's book, "Perestroika," appeared in bookstores here. "It's very strange," Maeena said, "for a Soviet political book to be distributed in Saudi Arabia."

Apart from economic benefits, the Soviets' new ties with Saudi Arabia may help ease any tensions caused by a revival of Islamic religious feelings in the Soviet Union, Maeena said. "The Saudis can play a very soothing, calming role with the Moslem population of the Soviet Union."

Most Saudis say they are pleased with the renewal of ties, and some note with satisfaction that it was done before Moscow normalized its relations with Israel. The Soviets maintain only a consulate in Israel.

Jiddah-based businessman Abdullah Ali Reza said that the new ties "are a natural phenomenon" given that the Soviet Union "is not too far away from us." With the new world order, he added, "we are going to have relations based on natural interests, economic interests."

As for Saudis rushing to invest in the Soviet Union, "most people are taking a wait-and-see attitude," said Ali Reza.