THE SOVIETS are back in the Middle East and nobody in the region, not even the most conservative Arab regimes, seems very worried. A decade of American supremacy is fading away and very few seem to regret it.

The new Soviet push in the Middle East is evident on several fronts:

Moscow's prosposal for an international conference to solve the Arab-Israeli conflict, yesterday viewed as an archaic Soviet non-starter, is now seriously considered as the way out of the present impasse by George Shultz, Shimon Peres and a number of Arab kings and presidents. Having secured a seat at the peace table, Moscow is understandably much less in a hurry to convene the conference, until some order is brought back to the Arab house. Meanwhile, nobody dares to mention anymore a unilateral American "peace process."

The Persian Gulf, once an "American lake" in strategic terms, is now a place where Soviet help is fervently sought -- not only by arms-thirsty Iraq but by pro-western oil countries increasingly worried by the threat to freedom of navigation. Moscow has recently established diplomatic relations with Oman and the United Arab Emirates. And while the Soviets haven't yet opened an embassy in Riyadh, three Saudi ministers have visited Moscow in less than two years to discuss sensitive issues such as oil pricing and the Arab-Israeli conflict.

The Soviets have made inroads in other countries. In Egypt, there is growing pressure for the government to take a more non-aligned stand in world politics. In Lebanon, Moscow has gained from the American disarray and has adroitly championed the implementation of United Nations resolutions while deftly diversifying her links with the various sectarian factions. In Sudan, staunch pro-Americanism has followed President Numeiry into exile. And in Iraq, the regime would have collapsed years ago if it were not for the quasi-permanent flow of Soviet weapons.

Moscow has been trying hard to ease the numerous inter-Arab conflicts. With Algerian help, it has achieved a reunification in the PLO's ranks. And the Soviets have encouraged a few limited steps towards Syrian-Iraqi reconciliation. The Soviets have also distanced themselves from Libyan setbacks in Chad while taking propaganda advantage from last year's U.S. attack on Tripoli.

Arabs are now more willing to deal with the Soviet Union in part because they don't regard Moscow as a threat. Most Arab governments tend to view Islamic fundamentalism as more destabilizing these days than Soviet atheism. And the Arabs, spoiled as they are by a decade of lavish buying of the West's latest inventions, could hardly be impressed by Soviet technology.

Moscow is making gains largely because of Washington's failure to offer an alternative. Socialist ideas are not suddenly triumphant and the Arabs are not really infatuated with Soviet achievements. The pivotal fact is that the Middle East is plagued with a number of intractable conflicts. For many years, the United States seemed willing and able to help solve them. But the Reagan administration has abdicated this role, and the Arabs are now quietly looking for alternatives.

Under Reagan, Washington failed to take advantage of the enormous influence the United States had enjoyed in the Middle East during the late 1970s. From Nixon through Carter, the United States had pursued the same basic objective: doing what it could to defuse the Middle East conflict and, in the process, closing the door on Soviet activity in the Middle East. Most Arabs hated this pragmatic approach, either in the form of shuttle diplomacy by Kissinger or beautiful speeches by Carter. Many Arabs, however, came to think of American diplomacy as the only option left to them.

The Reagan administration failed to follow up. As a result, the American balance sheet for the last six years has been one of lost opportunities and embarrassing misadventures. And the administration's hard anti-Soviet line in the region has been interpreted by many Arabs as an easy way to escape from an active conflict-resolution role.

Here's how Reagan's Middle East policy looks to many Arabs:

Instead of building upon the Kissinger-Carter efforts, the Administration behaved as if the Arab-Israeli conflict were too marginal to deserve serious attention. The administration repeatedly gave credence to the fashionable idea that certain conflicts are insoluble -- and eventually just fade away.

Instead of reestablishing some balance between Israel and the Arab world, Reagan chose to strengthen Israeli military supremacy, and signed a "strategic cooperation" agreement with Israel. As a result, American arms sales to the moderate Arabs began to dry up -- even as Moscow was replenishing the arsenals of its clients.

Instead of playing a moderating role in Lebanon (as it did in 1958), the United States gave an "amber light" to Israeli Gen. Ariel Sharon to invade that country. An embarrassed Reagan administration later sent the U.S. Marines to Beirut, but they failed to perform their role, if they were really assigned one. Instead of pushing for a rapid Israeli withdrawal (as it did in 1956 in the Sinai), the United States adopted an ambiguous policy in South Lebanon that boiled down to a "let Israel do it" attitude.

Instead of trying to find an early solution to the Iraq-Iran war, Washington adopted the Israeli point of view, which held that the longer this war went on, the better. In the process, Washington ignored the obvious risks of extension of the conflict, not to mention the growing disruption of shipping in that vital waterway.

Capping this sad story was the double game played with Iran by the administration's amateur Islamologists, Ollie North and Bud McFarlane. The Iran fiasco alienated all established governments in the region.

The American moment in the Middle East is ending. The pro-western Arab countries have learned a lesson they will not soon forget: It is very dangerous to follow the late President Sadat's advice and put 99 percent of your cards in Washington's hand. Washington may play them in the wrong game, or just fail to play them at all.

Ghassan Salame is a professor of political science at American University of Beirut and currently a visiting professor at the University of Paris. His new book, "The Foundations of the Arab State," will be published this fall.