The rulers of Saudi Arabia, recovered from their shock at Egyptian President Anwar Sadat's startling peace initiative, are now giving him strong support.

They are doing so, according to informed sources here, partly because they want a Middle East peace settlement on the terms Sadat is seeking and partly because he left them no other choice - just as he calculated when he decided to go to Isreal.

The Saudis are not confident that Sadat will succeed in achieving a peace agreements that other Arabs could accept. The message they delivered to President Carter during his brief visit this week was that Sadat needs U.S. help, in the form of a blunt message to Isreal on the need to withdraw from all territory occupied in the 1967 war and granted self-determination to the Palestinians. But if there ever was any serious possibility to overt Saudi opposition to Sadat's initiative, it has receded.

Sadat's visit to Jerusalem, made shortly after a trip here in which he did not tell the Saudis what he was planning, divided the government and led to sharp criticism among some elements of the Saudi leadership, according to informed sources. While the Saudis generally refrained from critisizing Sadat in public, there were strongly held views in private that Sadat had made a serious tactical error.

The innately cautious and canservatives royal rulers reportedly resolved the issue in Sadat's favor, fearing that if they did not, it could lead to Sadat's downfall and replacement by a less congenial ruler in Egypt, to a resurgence of Arab radicalism or to a strain in the Saudis' carefully cultivated ties to the United States.

"There was never any dispute over Sadat's objectives," said a well-placed Saudi official who was among the critics of the Jerusalem trip. "The question is over tactics. He made mistakes."

As is often the case where the Saudis are concerned, there were more elements to be weighed in judging in Sadat's move than political or international considerations. The Saudis takes seriously the religious and symbolic implications of their policies and are sides in disputes among the Arabs. According to this Saudi official, Sadat's moves stirred criticism on several of these grounds.

First, he said, Sadat should not have prayed at Jerusalem's Al Aqsa Mosque, a holy shrine of Islam, under Isreali military protection. In addition, in the views of his Saudi critics, Sadat insulted the other Arabs by his repeated assertions that Egypt was the heart of the Arab world and that the other Arabs could not act without Egypt.

Then he embarrassed Saudi Arabia, which has come to enjoy the role it has assumed in recent years as a political power in the Arab world which the experts respects as a financial benefactor that keeps Egypt afloat. Finally, the critics have said, Sadat made a mistake by playing the Arab's trump card - recognition of Isreal without any assurance that he would get a satisfactory return.

Once it became clear that Sadat was determined to forge ahead whether the other Arabs like it or not, however, the Saudis began to come down on his side. They have not spoken out in favor of his trip to Jerusalem, but are apparently satisfied that the terms he is demanding as the price of peace are terms acceptable to them.

The Saudi leadership is said to have been reassured by the outcome of the Christmas summit in Ismailia between Sadat and Isreali Prime Minister Menachen Begin - not because the results were positive but because it became clear the Sadat was sincere in saying he would not settle for a bilateral peace treaty with Isreal.

If Sadat has bolted to a separate peace it would have put this country in an intolerable position, observers here believe. The Saudis would have had to choose between Egypt on one hand and the rest of the Arabs on the other, which is just the kind of choice the Saudis did not like to confront.

Crown Prince Fahd, the most powerful policy maker in the kingdom, told an American television interviewer during Carter's visit that even if this country and the United States were not in full agreement on the terms of a peace settlement, he was pleased that Carter was stopping off to see Sadat. The Saudis were reassured that the United States also opposes a bilateral Egypt-Isreal treaty and apparently succeeded in moving the Americans closer to the Arab position on the terms of peace.

As defined by a Senior Foreign Ministry official, the terms acceptable to the Saudis are virtually identical to those being sought by Sadat - an agreement in principle that Isreal will eventually withdrawal from all occupied territory, with the details and implementation to be worked out over time if necessary, self-determinationfor the Palestinians and permission for large numbers of them to return to the West Bank, and restoration of the least token Arab control over Al Aqsa and other Islamic shrines of East Jerusalem.

Having decided that sadat is on the right track, the Saudis are now beginning to use their enormous to bring the United States, and the other Arabs, around the same position.