Saudi Arabia's King Fahd yesterday left Washington for home with the understanding that the United States is prepared to reengage in serious Middle East diplomacy if the current Jordan-Palestine Liberation Organization maneuvering produces a unified Arab position, according to a senior Saudi official.

The potential U.S. role in the next round of Arab-Israeli diplomacy was a central question on the mind of Fahd and his top aides in their talks here with President Reagan and key U.S. foreign policy officials.

As a result of the discussions, which included two working sessions with Reagan and lengthy discussions with Secretary of State George P. Shultz and national security affairs adviser Robert C. McFarlane, Saudi emissaries are preparing to pass the word to others in the Arab world in the days ahead that "the United States will bear its responsibility in a serious negotiation," according to this source.

Prince Bandar bin Sultan, Saudi ambassador to the United States, is flying to Damascus this weekend to inform Syrian President Hafez Assad of the Washington discussions, it was reported last night.

None of the leading Saudis whose views could be obtained said that specific commitments had been made by Reagan or his aides about the substance of a U.S. role in potential new Mideast negotiations. The Saudis said they were encouraged, though, by the thrust of the U.S. stand in the discussions here.

Both U.S. and Saudi sources remained cautious about whether the "framework for joint action" agreed on Monday by King Hussein of Jordan and PLO chairman Yasser Arafat will be endorsed by PLO decision-making bodies and fleshed out through further discussions to the point where a detailed offer could be made to Israel to undertake a new round of Arab-Israeli negotiations.

Senior U.S. and Saudi officials seemed to agree, though, that such a development is within the realm of possibility. In public as well as private, the Reagan administration is taking it seriously. The Saudis are saying little or nothing in public but are reported to be working behind the scenes to facilitate an agreement.

Fahd, who left Andrews Air Force Base yesterday after five days of meetings, was described by Saudi officials as well satisfied with his rapport with Reagan and the cautious but "constructive" answers about Mideast diplomacy that he received from his U.S. interlocutors.

"In the future you will see openings happen in the Mideast as a result of this visit," a key Saudi official involved in the discussions told a group of reporters. The official, who asked not to be quoted by name, said some of the "openings" may occur in Lebanon but was not specific about other areas.

Fahd was presented with a "very strong commitment from the president and the whole administration on the importance of the security of Saudi Arabia," a Saudi official said. He expressed confidence that the current U.S. review of major arms sales to the Mideast "will enhance our arguments" for the sale of 40 more U.S. F15 fighters to the oil kingdom. He said the details of the next warplane sale had not been discussed in the Fahd talks.

The Defense Department, saying there was no connection with the Fahd visit, announced plans to strengthen Saudi air defense through the sale of a $250 million system that can distinguish between friendly and hostile aircraft. A Pentagon announcement said the sale "will contribute significantly to U.S. foreign policy and national security objectives by helping to increase the security of a friendly country of vital interest to the United States."

Another aspect of the Fahd discussions involved next week's talks on Middle East issues in Vienna between the United States and the Soviet Union. On this point, the State Department went out of its way once again yesterday to caution reporters against "any inflated expectations." Reporters were told at a State Department briefing on the U.S.-Soviet talks that no information about them will be disclosed next week in Vienna and that there are no plans for follow-on talks. The United States, through such a low-profile stance and a series of diplomatic messages, hopes to convince Mideast nations that the Vienna talks are not intended to work out U.S.-Soviet deals in the area.

The Soviets are expected to raise their call for an international conference on the Middle East, according to the State Department briefer. The U.S. delegation headed by Assistant Secretary of State Richard W. Murphy will reply that Washington's assessment of the possibilities of a Soviet role in the Mideast peace process will depend on "steps the Soviets take to show their sincerity."