Saudi Arabia's powerful leadership has asked the UnitedStates to move toward recognition of the Palestine Liberation Organization in order to break a political logjam standing in the way of a new Geneva peace conference.

This request, according to authoritative Saudi and U.S. sources, was made by Crown Prince Fahd and other leaders of the oil-rich kingdom in lengthy meetings with U.S. Secretary of State Cyrus R. Vance yesterday in Riyadh. Vance left Riyadh today for Damascus, the last stop on his Middle East tour.

"The Arab world has been doing all it can toachieve the conditions which will lead to peace. It can't do much more without movement on the Israeli side, and central to that movement is the position taken by the United States," Prince Saud the Saudi foreign minister, said in an interview.

Clearly expressing the deep apprehension about Middle East stability that underlies extensive Saudi diplomatic efforts on the surface and behind the scenes, Saud added: "If there is no movement toward peace int he area, conditions (in the Arab countries) will deteriorate very quickly to the detriment of everybody's interest." He said he and other members of the royal family delivered the same message to Vance in forceful terms in yesterday's closed meetings.

In keeping with a secret pledge given in writing to Israel late in 1975 by former Secretary of State Henry A. Kissinger, the United States has refused to reorganize or negotiate with the PLO until that organization recognizes Israel's "right to exist" and approve U.N. resolutions 242 and 328, which Israel interprets as supporting its right to exist. A change in this U.S. position is unlikely without some PLO action that could justify the shift. Vance gave no promise to the Saudis yesterday that he will take the action they requested.

Saudi Arabia, Syria and Egypt are believed to have it within their power to force the PLO to recognize Israel openly, at least on a defacto basis. But the Arab states are reluctant to dictate drastic new changes in the PLO political stance in the absence of evidence that Israel will reciprocate with changes of its own.

Saudi leaders and Syrian President Hafex Assad, whom Vance saw here today, believe that the United States, as Israel's chief international backer, is the key to changes in Jerusalem. The leaders of these two Arab states fear that Israel will refuse to move toward an accommodation with the palestininans, throwing impediments in the way of agreements with the Arabs rather than taking the risks an Arab-Iraeli compromise would bring.

In an airport ceremony before Vance left Riyadh this morning, the Saudi foreign minister told Vance publicly that his country is optimistic about peace prospects for two reasons:

First, because the Secretary of State's mission to the Middle East in this early stage of the Carter administration indicates U.S. determination:

Second because "you yourself (Vance) expressed that at the core of the Middle East problem is the Palestinian question."

Vance, responding before television cameras and reporters, said:

"I agree that there is a basis for optimism but I must caution that the road ahead will be a long and difficult one".

In an effort to soften the impact of Saudi's concentration on the delicate Palestinian issue, Vance added: "It is true the Palestinian question is one of the core questions that must be the subject of continuing discussion with Saudi Arabia and other countries."

In answer and reporter's question, Saud denied that the Saudi decision to limit oil-price increases to 5 per cent for 1977 was taken in the hope that the United States would exert pressure on Israel to make accomodations with the Arabs.

Saud called last December's oil-price decision, which shattered the unity of OPEC, "an economic decision" based on Saudi regard for the international economic situation. At the same time, he said "Our policy in everything we do is geared to and aimed at stability and at improving the prospects for peace in the Middle East."

The Carter administration has said publicly that no commitment on Middle East peace had been made to Saudi Arabia in return for its restraint on oil prices. Nevertheless the two issues have been linked in public statements by Saudi Petroleum Minister Sheikh Zaki Yamani and in comments by many independent observers of the Middle East scene.

During yesterday's meetings with Vance, the Saudi leaders expresed their view that some types of pending U.S. Legislation against the Arab boycott of Israel would bring drastic consequences to U.S. Saudi trade relations if enacted.

Saudi leaders said they told Vance they are willing to consider complaints of boycott injustices to American companies if these are presented through diplomatic channels, but that legislation striking broadly at the long-standing boycott of Israel could severely complicate Saudi-U.S. trade.

The Saudi leaders also stressed to Vance their request for U.S. action to mitigate the financial problems of the less-developed world. They called the proverty of the low-income nations "a time bomb" that could eventually endanger rich nations such as the United States and the oil shekdom, Saudi participants said.