Prince Fahd, Saudi Arabia's key decision-maker, expressed increased interest today in U.S. efforts to gain Palestinian autonomy in Israeli-occupied Gaza and the West Bank, high U.S. officials said.

Fahd and the Saudi foreign minister, Prince Saud, received a report on the autonomy negotiations from President Carter's special Middle East envoy, Sol Linowitz. For the first time, Linowitz was able to claim some success on points of substance, arousing what the officials portrayed as a new level of concern for the talks among Saudi leaders.

It was difficult to gauge how much of the Saudi attitude was traditional Bedouin hospitality and eagerness to please a guest and how much was genuinely increased interest in the Egyptian, U.S. and Israeli effort to organize self-rule in the occupied territories.

But Linowitz and his aides, who left Riyadh ahead of schedule for a stop in Morocco and talks there with King Hassan, clearly were buoyed by the outcome of his 3 1/2-hours of meetings here, first with Saud and then with the two princes together in Riyadh's ornate pink palace.

The Saudi attitude is considered critical to any hope of success in the nine-month-old talks. Without Saudi Arabian approval, the outcome would be unlikely to win acceptance from West Bank Palestinians, Yasser Arafat's Palestine Liberation Organization or King Hussein of Jordan, who ruled the West Bank until 1967.

Linowitz' reception was judged favorable by U.S. officials in the light of signs on his arrival last night that the Saudi royalty intended to express its longstanding coolness toward the Egyptian-Israeli peace treaty and the negotiations set up under the Camp David accords. In addition, diplomats here said, the Saudis had looked askance at Linowitz' appointment as Middle East envoy because he is Jewish. Robert Strauss, Linowitz' predecessor as special envoy, also is Jewish.

As Linowitz arrived and drank bitter Bedouin coffee poured as a welcoming gesture, King Khalid sent word he was too busy seeing Saudi tribal sheiks in the desert to receive him. At that point, Fahd also was out in the desert and still had not sent definite word that he would make it back to Riyadh in time for Linowitz. Only Saud, the Princeton-educated foreign minister, had agreed to a meeting -- and even his aides had yet to fix a firm time.

By the time the stay was over, however, Linowitz had seen Fahd and Saud and proclaimed himself encouraged by Saudi reaction to his report. Although they declined to specify why, U.S. officials said the Saudis had listened with unusual interest to Linowitz' account of U.S. aims in the talks and his claims of success in this week's negotiating session in Israel.

"I told them the talks have the hope of achieving full autonomy for the Palestinians and that we have had enough encouragement so far to make it worth our while to continue on the same path," Linowitz said. "They did not argue with me."

U.S. officials made no claims however, of having overcome overall Saudi skepticism about the Egyptian-Israeli talks. The Saudi royal family has insisted that President Anway Sadat's peace accord with Israel was a mistake because, in the Saudi judgement, it cannot achieve a peace settlement acceptable to the other Arabs. j

In particular, the Audis have expressed doubt that Israel will be persuaded in the talks to agree to a Palestinian state and renewal of Arab sovereignty over East Jerusalem -- both fundamental ingredients of an acceptable peace in Saudi eyes.

Neither of these crucial Saudi demands was covered in the group of self-rule powers agreed on in the round of Egyptian-Israeli negotiations Wednesday and Thursday in Herzlya, a suburb of Tel Aviv. U.S. officials said that Linowitz nevertheless elicited Fahd's attention by pointing out that the agreement marked at least a first step on points of substance concerning Palestinian self-rule.

Neither Fahd nor Saud are reported to have expressed rancor about the vehement criticism leveled at them recently by Sadat, underlining instead their assessment that his peace with Israel will prove unable to produce a satisfactory accord on Palestinian demands for statehood, U.S. officials said.

This was considered a sensitive point in Linowitz' talks here because he saw Sadat last Monday in Cairo only a few hours after the Egyptian leader again publicly denounced the Saudis for opposing his policies.U.S. diplomats had expressed concern that the coincidence could cast a pall over Linowitz' mission here.