Having shattered the facade of Arab unity and generated intense concern among many Arab leaders for their own survival, the Iraqi-Iranian war is now presenting Egypt's President Anwar Sadat with his first real opportunity to break out of the isolation imposed upon him two years ago for making peace with Israel.

There are small but significant signs that the first step out of this isolation may well be a rapprochement between Egypt and Saudi Arabia, which has just broken diplomatic relations with Libya and moved closer to the same kind of overt military alliance with the United States as President Sadat is openly promoting.

These signs include the sending of secret Egyptian emissaries to Saudi Arabia recently under the guise of the annual pilgrimage to Mecca, an end to Sadat's vitriolic attacks on the Saudi royal family and his offer to provide military assistance to any Persian Gulf state requesting it.

"There is already a de facto rapprochement," said one high-ranking Egyptian official who suggested this might be sufficient for the time being.

Such a rapprochement could well be the biggest longterm American dividend from the seven-week-old Iranian-Iraqi war. It would bring together the United States' two most important Arab allies in a military and political alliance Washington could use as a springboard to project its power into the vital gulf region in a far more effective way than it can today.

The Carter administration has been quietly involved for some time in promoting such a rapprochement, and the war has offered U.S. officials an excellent opportunity to prod the Saudis more forcefully in this direction.

In early October, Gen. David C. Jones, chairman of the U.S. Joint Chiefs of Staff, visited both Saudi Arabia and Egypt and was reported here later to have told the Egyptian officials that the Saudis were now ready to cooperate to protect their oil fields, particularly from the Soviet threat, which loans so large in Saudi minds.

Disclosing the new Saudi readiness, Egypt's chief-of-staff, Gen. Mohammed Abu Ghazala, told the authoriative Cairo daily Al Ahram that Washington was acting as the chief intermediary. But he cautioned: "It is premature to talk about any details or the extent of the cooperation because we are still negotiating. We are still discussing and we haven't come up with a solution yet."

In the view of both Western and Egyptian analysts, the main obstacle is finding a face-saving formula that would allow the Saudis to identify themselves openly once again with Sadat after having broken with him over Camp David and in face of his clear determination to proceed with the normalization of relations with Israel even in the absence of any progress in the Palestinian autonomy talks.

"It is a challenge," remarked one Egyptian political commentator close to Sadat. "Either they are right or we are right."

"We cannot take the initiative," said a Foreign Ministry official. "They broke relations and they should take the initiative to have a rapprochement."

Thus it appears Arab pride and concern about loss of face still remain major barriers to better relations between what the United States considers the two most strategic Arab nations, militarily and politically, in the Middle East.

The pride of this nation and its leader could not have been more openly displayed than in Sadat's speech Saturday at the opening session of the Egyptian parliament.

He made an appeal to the Arab world to recognize the error of its ways in trying to isolate Egypt and called upon it to rally behind Egyptian leadership once again.

He ridiculed the political "acrobatics" of virtually all Arab leaders since their decision to cut off relations with his country in 1979 over the Camp David accords and said their attempt to isolate Egypt had resulted in the fragmentation of the Arab world into warring factions and general political instability.

"The result of the Arab decision to isolate Egypt was to isolate themselves," he said, reviewing all the inter-Arab squabbles of the past two years and new divisions arising from the Iraqi-Iranian war.

He called Iraqi President Saddam Hussein the clear "aggressor" and accused him of having illusions of grandeur in aspiring to become the leader of the Gulf and "the Middle East as a whole."

Sadat asserted that Egypt alone now has the political stability and military might to play this role in the wake of the Iranian-Iraqi war, and he again appealed to other Arab leaders to join with him in the search for a comprehensive Middle East peace and in devising a "new outlook and plan" to deal with the Palestinian problem.

One theory of how Egypt and at least part of the Arab world might be reconciled is that it will come about through a new European initiative to break the present deadlock in the Camp David negotiations over autonomy for the Palestinians on the Israeli-occupied West Bank and Gaza Strip.

Sadat is clearly counting on such an intiative to fill a time gap that it is believed here may stretch as long as a year -- until after Israel holds its elections -- before any real progress is made toward a final Middle East peace settlement.

Egypt's deputy foreign minister, Butros Ghali, recently stated that Cairo will support Europe in this new peace endeavor "on condition that it goes along with Egyptian diplomatic efforts."

If Saudi Arabia and a sufficient number of other Arab states also backed a European initiative this could provide the common ground now missing for their rapprochement with Egypt, even if it produced no immediate progress in the autonomy talks.

The prospects for such a possibility may become clearer after the next Arab summit, still scheduled to take place, despite the turmoil in Arab politics, in Amman, Jordan in mid-November.