Despite initial unhappiness over President Anwar Sadat's surprise decision to visit Israel, Saudi Arabia has privately thrown its powerful support behind the Egyptian leader's peace initiative, diplomatic sources said today.

The Saudi decision to back Sadat's historic mission was expected to undercut efforts by Syria and other hard line Arab states to form a united front in opposition to the Egyptian president that would leave him isolated in the Arab world.

The first sign of a softening of Arab opposition to the Sadat peace bid came today when the Palestine Liberation Organization's representative, Zahdi Labib Terzi, refrained from any direct attack on Sadat in a surprisingly mild address to the U.N. General Assembly.

In sharp contrast to yesterday's highly personal denunciation of Sadat by Syria, which provoked an Egyptian walkout from the General Assembly, Terzi merely read previous statements by PLO leader Yasar Arafat opposing the Jerusalem talks.

"He really left Syria way out on a limb all by itself," remarked a U.S. diplomat. As the U.N. General Assembly continues its annual Middle East debate this week, he said, "I think we're going to see a strong reaction building to give Sadat and (Israeli Prime Minister Menahem) Begin a chance."

Diplomatic sources said today that both in bilateral talks and in a meeting of the Arab group here, Saudi diplomats have been "very supportive" of Sadat's mission to Israel.

"At first, the Saudis weren't too happy about the visit," a U.S. official said. "They really didn't like Sadat going to Jerusalem - in particular because of the religious side of things."

Saudi Arabia has long considered itself the guardian of the Moslem holy places in Jerusalem. Saudi King Faisal, who was assassinated in 1975, often stated his hope of worshipping in old Jerusalem's Al Aqsa Mosque - the third holiest shrine in Islam - after its return to Arab sovereignty.

But while Saudi Arabia initially voiced mild criticism late last week of Sadat's trip, sources said that the Saudis quickly decided privately that they must support Sadat's peace initiative to prevent Arab diplomatic policy from falling into the hands of radicals.

"We can't permit Sadat to be weakened," a senior Saudi diplomat told one U.S. delegate.Saudi support for the Egyptian leader increased, sources said, following Sadat's speech to the Knesset.

"The Saudis are saying that Sadat couldn't have given a better statement," a U.S. official said. "They are saying that he gave a full and fair presentation of the Arab view. It was very strong."

U.S. officials conceded, however, that they will feel even better when King Khaled himself issues a strong statement backing the Egyptian leader.

The first public indication of Saudi Arabia's rethinking of its position came in Cario today.

Saudi Arabia's charge d'affaires there met with Egyptian Acting Foreign Minister Boutros Boutros-Ghali to discuss the Sadat trip and told reporters afterward, "I personally am satisfied." He said, however, that he did not know what position his government would take on the matter.

The PLO's Terzi, in his address to the General Assembly today, spared few adjectives in his denunciation of the "racist Zionist state" of Israel and the "notorious terrorist" Begin. But he refrained from adding critical adjectives to references to "the president of Egypt."

Some diplomatic sources suggested today that the PLO - recalling the serious consequences of its last split with Egypt two years ago over the Sinai II accord - might be having second thoughts over the wisdom of breaking with Cairo and throwing its lot in with the Syrians.

"Two years ago, the PLO threw their hat in with the Syrians and in the next year, they were almost decimated - they lost 30,000 men in the civil war in Lebanon," a U.S. source said. "There's no way that the PLO is going to count on Syria alone again."

Late today, Egyptian Ambassador A. Esmat Abdel Meguid addressed the General Assembly and emphasized that Cairo would only agree to a Middle East peace settlement that included "the right of the Palestinian people to self-determination and to establish an independent state of its own."

Meguid in his address told U.N. delegates that they had witnessed last weekend Egypt's acceptance of "the challenge of peace."

"What Egypt is seeking - and the entire world stands witness to its intentions - is a just peace for the whole Middle East area," Meguid said, "not a peace that would be achieved at any price, not a unilateral peace settlement."