The Arab world, humiliated to its sensitive marrow by Israel in Lebanon and by Iran in the Persian Gulf war, is now turning to the United States for its political salvation.

That the Arabs should look for salvation from the country regarded as the best friend of their archenemy, Israel, is just one of the many paradoxes created by the Israeli invasion of Lebanon and its aftermath.

But the massacre of Palestinian civilians in West Beirut, the Israeli occupation of the city in violation of its own agreement with Washington and the murder of Lebanon's president-elect Bashir Gemayel have only strengthened the Arab conviction that Israel has become an extreme menace to the stability and security of the entire area. The more Israel appears out of control and uncontrollable, the more Arab leaders are looking to Washington for help. They are not acting out of faith in the United States, but rather out of desperation.

At the same time, the Arabs are heartened by the appearance of unanticipated differences between the Reagan and Begin governments that raise for them the prospect that America may finally be willing to use its power to bring Israel under control.

There is more behind this new mood of accommodation with the United States than raw fear of Israel. The Arab world is awash today in deep currents of religious and political extremism born of defeat and frustration that threaten to sweep away America's best Arab friends.

Virtually all Arab leaders now live in fear of terrorism. They must be wary of Islamic extremists inspired by Iran's revolution, and of embittered Palestinians and other radicals seeking revenge for perceived Arab betrayal of their cause.

King Hassan of Morocco has warned of a decade ahead of "blind terrorism without limits or ideology" arising out of the war in Lebanon and threatening the whole world. His ansieties are shared by moderates and militants alike in the Arab world today.

Even Syria, the key radical confrontation state, has now joined the moderates in seeking Washington's help. It wants to come in from the cold diplomatic isolation where it has been for years, thanks partly to a cold shoulder from Washington but also partly to its own misguided faith in Soviet arms and protection.

With half his air force shot out of the skies over Lebanon by American-made, Israeli-piloted aircraft and his army terribly exposed in the Bekaa Valley, President Hafez el- Assad has announced he is ready to get out of what Syria has always regarded its special preserve in Lebanon.

Washington, Assad realizes, holds the key to an honorable Syrian withdrawal from Lebanon, linked, he hopes, to one by Israel as well.

Even for Assad, who has built his whole foreign policy on rejection of the Camp David accords and U.S. peace plans, the only option left is the "American card."

Not only has the Syrian leader agreed to back a peace plan put forward by Saudi Arabia, one of America's key allies, but he has carefully avoided attacking the Reagan peace initiative, despite the reservations he must feel.

It may have been a symbol of changing Syrian attitudes toward the United States that Assad's brother, the number two man in the Syrian regime, recently bought a home in the Washington suburbs and enrolled his children in school there.

The Arabs today are forced to turn to Washington as the last hope not only for the battered Palestinian cause, but for the survival of many of the Arab world's contemporary rulers.

The Arabs' willingess to turn to Washington for help is a product of several factors: the Arab perception of Israel as an unrestrained superpower; the exposure of the Soviet Union as a paper tiger; and partly, too, the eleventh hour American awakening to the catastrophe brewing in the region.

But the most fundamental factor is Arab impotence, which today is more than just military. The persisting oil glut has undercut perhaps the Arabs' most important potential source of international leverage. Threats of a new oil boycott ring exceptionally hollow when even Libya, the region's most unrepentant radical, is scrambling to find markets for its oil and offering cut prices to refill empty government coffers.

A signal of the new pan-Arab desire to work with Washington came at the recent summit in Fez, Morocco. To outsiders the signal may have been ambiguous, but in Arab terms it was unmistakable.

At Fez, not a bad word was said about President Reagan's peace plan. More important, Arab leaders, with only one exception, responded to Reagan's plea for Arab recognition of the "reality of Israel" by declaring openly that all nations in the region should be guaranteed the right to live in peace.

For the Arabs, notably the radicals, this was a big step, particularly given the president's explicit refusal to support an independent Palestinian state, which has been a keystone of Arab rhetoric since the creation of Israel.

As recently as last November, Syria had boycotted an earlier Fez meeting because of its opposition to a provision of a new Saudi peace initiative that implicitly recognized Israel, and a divided PLO then allowed Syria to bury that Saudi initiative. Now , just ten months later, the Arabs (minus Libya) have agreed on a peace plan for the first time since Israel was created. And they have let the Reagan plan sit on the table without any direct criticism of it. In Arab terms, these are significant departures from past policies.

Though awash in oil walth and a material opulence undreamed of only a decade ago, the Arab world is also near bankruptcy in terms of political leadership and ideology.

No leader has come forward to fill the giant shoes of either Gamal Abdel Nasser, the charismatic Pan-Arab hero who led the Arabs in war against Israel, or those of Anwar Sadat, who tried to show the way toward peace.

Indeed, the entire older generation of Arab leaders, those who have been in power a deacade or more, are all perilously close to exhaustion from internal upheavals, lost wars or failed ideologies. This includes onetime radicals Saddam Hussein of Iraq, Hafez Assad of Syria, and Muammar Qaddafi of Libya as well as Jaafar Nimeri of the Sudan, King Hassan of Morocco and King Hussein of Jordan, all moderates.

None has been able to sustain a political vision of the future or convincing ideology to galvanize the hearts and minds of the Arab people. Instead, the great hope for a renaisance among the disgruntled and humiliated of the Arab world has come from Iran -- a Persian nation historicaly viewed as an Arab enemy -- in the form of a fiery Islamic fundamentalism preaching the overthrow of most Arab regimes in favor of new Islamic republics.

The first victim of this new Moslem militancy was Sadat, slain by extremists last October as he watched a military parade. Both Assad of Syria and Saddam of Iraq, rival leaders of the Arab Socialist Baath Movement, are also locked in a battle for survival against the new wave of fundamentalism sweeping the Arab world.

The sheikhs and kings of the Arab oil heartland across the gulf from Iran are under similar pressure. Even King Hussein of Jordan feels threatened indirectly by this Islamic militancy because it aims at bringing down his closest allies.

To this religious "threat" has now been added the political one of a deeply embittered Palestinian guerrilla force scattered across the Arab world. The Palestinians feel betrayed by impotent Arab leaders who failed to use either their presumed politcal or economic leverage with the United States to stop the Israeli invasion of Lebanon or the carnage in Beirut.

Indeed, not a single Arab country, not even Libya, publicly threatened Washington with political or economic reprisals throughout the long, hot Lebanese summer.

It is the pervasive fear and insecurity of Arab leaders, together with the realization that there really are no options left, that has driven them to the doorstep of the White House in search of shelter from the triple whirlwinds of Islamic fundamentalism, Palestinian fury and Israeli military might.

President Reagan's speech of Sept. 1, setting the United States squarely against Israel's policies in the occupied Arab territories, opened up new opportunities for diplomatic maneuvering that Arab leaders desperately needed in the wake of Lebanon.

The moderates, led by Saudi Arabia, Morocco and Jordan, had long argued for a concerted diplomatic strategy aimed at splitting Washington from Tel Aviv. But not until the de facto collpase of the militants' "steadfastness front" in the ruins of Beirut was such a wider consensus possible.

The front, consisting of Syria, Libya, Algeria, South Yemen and the PLO, was set up in the wake of Sadat's historic trip to Jerusalem in November 1977 to block his peace policy toward Israel. It had heretofore stymied the moderates in their half-hearted efforts to move toward an Egyptian-style accommodation with Israel.

The disintegration of this front was very much in evidence at Fez. While Assad and Arafat backed the Saudi-proposed peace plan, Qadaffi alone stayed away from the summit, while Algeria and South Yemen, whatever their reservations, went along quietly with its proposals.

Even during the summer, however, the discord among members of the steadfastness front was highlighted by Qaddafi's call for the PLO to "commit suicide" in Beirut rather than accept an American-sponsored evacuation plan. Today, the PLO is no longer even talking to Qaddafi.

President Reagan's new initiative suddenly offered the Arab world a ray of hope at a time of its maximum frustration and despair. No Arab leader expected an American president to come forth with a plan aimed at preventing Israel from permanently absorbing all of Jerusalem, the West Bank and Gaza Strip. They especially did not expect such a plan from Ronald Reagan, who came into office equating the PLO with pure terrorism, and who refused to call Israeli settlements on the West Bank "illegal."

The new Arab peace strategy -- if that term can be applied to the plans worked out at Fez -- calls for the creation of a committee of Arab leaders whose first task will be to take the Arab peace plan to Washington and other world capitals in search of support and discussion on other similar proposals.

The Arab leaders also intend to present their plan to the United Nations General Assembly in hopes of getting a ringing endorsement that will bring more pressure ot bear on both the Israeli and American governments.

King Hussein said in an interview with The Washington Post last week, however, that the main Arab objective now is to engage the Reagan Administration in a dialogue to try to find common ground that might serve as a basis for peace negotiations.

Vice President Bush last week criticized the Arabs for failing to state more explicitly their willingness to accept the existence of Israel, but for the Arabs the issue now is whether Washington will be able to pressure Israel to come to the negotiating table on American terms.

For the Arabs, the first test of American resolve will be here in Lebanon, where Israel has flouted its own agreement with Washington not to enter West Beirut, and made a mockery of U.S. guarantees for the protection of Palestinian civilians. If the Reagan administration cannot exercise decisive influence over Israel here, then its credibility as a peace broker within the Arab world is certain to be destroyed. Similarly at risk is the credibility of moderate Arabs arguing for a peace strategy based on the assumption that Washington can drag Israel into a realistic negotiating process.

If Washington does not do something soon, however, it may well see its best friends across the Arab world fall like dominos in the uncontrollable crosswinds of political and religious extremism buffeting this region. The moderates are pleading for help from Washington, but they are far from certain that President Reagan fully appreciates their plight.