The Soviet Union asked Syria to provide it with military "facilities" but the request was refused, according to a source present at Syrian President Hafez Assad's talks with Soviet leaders in Moscow last week.

While the Russians did not use the world "bases" in their request, the highly placed Syrian source said today that the intent was obvious.

"They wanted to establish military bases on our soil," he said.

Assad is to meet President Carter in Geneva May 9 to discuss possible solutions in the Middle East. According to the source close to the palace, the Soviets wanted Assad to come to Moscow after he met with Carter, feeling that the Syrian president might be easier to deal with if he failed to achieve any gains in the Carter talks. Assad reportedly insisted on going to Moscow first.

The sources said that Assad told the Soviet leaders that such a request made them no better than the "imperalist" powers they are always criticizing.

Despite the reported Syrian refusal, observers here believe that Assad's visit to Moscow was basically successful, easing the strain in relations between the two countries over Syria's military role in Lebanon.

The request came as the Soviets are consolidating their influence in the Red Sea. Somalia has given the Soviets limited base facilities for planes and ships in exchange for a flood of arms.

The Soviet Union also needs bases in the eastern Mediterranean for its 60-ship fleet, which has sailed those waters since the mid-1960s.The ships had been using the Egyptian port Alexandria, but now that relations between Egypt and the Soviet Union are strained. The Soviet navy needs new facilities for refuling and repairing its ships.

Since the Soviet navy does not have aircraft carriers equipped with fighter planes, it also needs nearby air bases for land-based planes that provide tactical support for its ships.

Syria has two small ports on its 100-mile-long Mediterranean coast - Latakia and a newly constructed port at Tartous.

The Syrian navy is the smallest part of Syria's armed forces. Of about 137,000 men under arms, only 2,500 are sailors and they are mainly concerned with coastal defense.

Soviet ships have called at the Syrian ports in the past, and use them for refueling and repairs, but they have no permanent bases or facilities there.

One of the promises the Soviets were reported to have made to Assad in Moscow was assist in improving the port of Latakia.

The Syrian leader also turned down a Soviet request to issue a statement supporting the invasion of Zaire by Katangan exiles from Angola, the source said.

"Every time the Soviets brought that up," he said, "President Assad started talking about support for the Eritreans" who are trying to split their area away from Ethiopia, an ally of Moscow. The Eritrean province is Ethiopia's only outlet to the Red Sea.

As a result, the source continued nothing was said in the final Syrian-Soviet communique about Africa.

Assad's refusal to give in to Soviet requests reflects his desire to maintain balanced relations with both the United States and the Soviet Union.

Syria was once one of the Soviet Union's closest allies in the Middle East, receiving all its military supplies from that country. At the same time Syrian's-Soviet relations cooled, Henry Kissinger's shuttle diplomacy reopened relations between the United States and Syria. While Syria is still feeling its way with the United States, Western diplomats here note that relations are constantly improving.

Before making up with Syria last week, Moscow was left with only Iraq and the Palestine Liberation Organization as allies in the Middle East.

Improved ties with the Soviet Union should help Syria's economy, under heavy pressure because of the cost of Lebanese peace effort and the loss of Iraqi oil.