Saudi Arabia spelled out for the first time today its strategy for gaining international acceptance of the eight-point plan presented by Crown Prince Fahd as an alternative to the U.S.-sponsored Camp David peace process.

In a press conference here after British Foreign Secretary Lord Carrington's two-day visit, the Saudi foreign minister, Prince Saud, said Saudi Arabia will seek a resolution at the United Nations endorsing the Fahd plan and then ask the Security Council to sponsor an international conference in which the Soviet Union would participate.

He also made clear, without explicitly saying it, that the plan's seventh point, which declares that "all states in the region" should live in peace, involved Arab recognition of Israel, an assertion that Israel has questioned.

Carrington, in Riyadh as a representative of the European Community, spent more than four hours yesterday discussing both the Saudi plan and the European stand on the Middle East. He told British correspondents traveling with him that it was "my firm conviction" that the Saudis were including Israel when they spoke of "all states."

Saud, a fluent English speaker, was repeatedly asked what precisely the Saudis meant by point seven and whether this included recognition of Israel. He replied:

"Point seven represents to our mind a logical result of the other points. The relevant factor here is the state of Palestine, and the other six points that are part and parcel of the seventh point go along toward clarifying that issue." Point six calls for establishment of an independent Palestinian state with Arab Jerusalem as its capital.

"As a result of accepting the principles of the establishment of the state of Palestine and having discussions between that state and Israel for achieving a peaceful settlement, we think that the guarantees that are called for in point seven reflect that aspect" -- recognition of Israel.

"There would not be negotiations between Palestine and Israel unless they mutually recognized each other, and that is the important factor," he added.

But Saud did not explicitly say that Saudi Arabia or any other Arab country was ready to formally recognize Israel provided an agreement was reached. Nonetheless, Carrington seemed to imply, and other diplomatic sources here confirmed, that the Saudis were ready to do so if Israel agreed to discuss the Fahd plan and agreement were reached.

Sources here said the Israelis have been told privately of the Saudi intention through an unnamed third party.

The Saudi foreign minister also told the British correspondents that Saudi Arabia was hoping the Reagan administration would come out more positively in support of the Fahd plan as well as working to persuade Israel to accept it.

Discussing the Saudi strategy for the plan, Saud at first said his country had no "strict framework" in mind beyond presenting it to the summit meeting of Arab leaders in Fez, Morocco, at the end of this month. But he quickly added:

"We've thought that one of the ways that could be used was to get one overall resolution in the United Nations based on the eight points as establishing a framework for the negotiations and then the negotiations would be held either through the Security Council or another international conference."

But he made clear the Saudi preference for a U.N.-sponsored meeting, saying that "because you have to have international guarantees then you must have some form of international representation and we thought the Security Council might serve a good purpose there."

Asked if Soviet participation in such a conference was envisioned, Saud replied, "Of course with the Soviet Union. It is part of the Security Council." It was not clear whether this approach excluded as a possible conference site a return to Geneva, where the United States and the Soviet Union had agreed to cosponsor negotiations for a Middle East settlement before the late Egyptian President Anwar Sadat made his historic trip to Jerusalem in late 1977.

The Saudi plan, unveiled in early August when Sadat was visiting Washington, demands that Israel withdraw from all Arab territories occupied during the 1967 Arab-Israeli war, "including Arab Jerusalem."

It also calls for dismantling of Israeli settlements on the West Bank and in other occupied Arab lands, recognition of the right of the Palestinians to return to their homes or be compensated for their properties if they do not wish to return, guarantees of freedom of worship for all religions in the holy places there and U.N. supervision over execution of the plan.

Israeli Prime Minister Menachem Begin Monday described the Fahd plan as a "liquidation formula" and said the eight points "cannot serve as any basis for any discussions whatsoever. They are rejected from start to finish."

The Saudis say the plan largely embodies a number of resolutions passed by the U.N. General Assembly and Security Council plus some additional points adopted at past Arab summit meetings.

The most interesting and controversial from the Arab view is point seven which states that "all states in the region should be able to live in peace."

This has been seized upon by Western European governments as well as the Reagan administration as something of a breakthrough in the Arab stand because of its apparent recognition of Israel, something only Egypt has been willing to do explicitly through its peace treaty with the Jewish state.

Saud appeared extremely confident that the Saudi plan was picking up momentum and would obtain the backing of most Arab states at the Fez summit, which opens Nov. 24. He said the reaction so far, particularly from the Palestinians, gave him "very high" hopes it would be unanimously endorsed there.

Palestine Liberation Organization leader Yasser Arafat visited Riyadh just before Carrington's arrival here and diplomatic sources and an Arab journalist who interviewed him said he was ready to back the Fahd plan fully.

Arafat also heads Fatah, the main faction in the PLO. At least three other factions backed by Syria have condemned the Saudi plan, but it is thought that Arafat can prevail within the PLO leadership if there is a showdown over it.

Syria at first condemned the plan, but after a visit to Damascus by a top Saudi leader, the government there has not been outspoken against it. Libya, with whom Saudi Arabia broke diplomatic relations in October 1980, has so far been the most outspoken opponent.

In addition to expecting broad Arab backing for the Fahd plan, Saud indicated the Saudis anticipated that the Reagan administration would play an important role in assuaging Israeli opposition to it.

He said he was hoping for a "more positive response" from Washington than it has so far shown and answered with a terse "yes" when asked whether Saudi Arabia was expecting the United States to persuade Israel to accept the plan.

The Reagan administration spoke warmly of the Saudi plan last week, but after sharp criticism by Israel, it pulled back and restated its support for the Camp David process, which Israel and Egypt pledged to pursue in the wake of Sadat's assassination.

The intense Saudi opposition to the Camp David accords was again made clear today by Saud, who called the Fahd plan "a very clear and sound alternative" to them. He also warned Europe against involving itself in the Camp David process through participation in the multinational peacekeeping force being set up to police the Sinai after Israel withdraws from there next April.

Part of Carrington's mission reportedly was to explain the European position on this issue as well as to explore the common ground between the Fahd plan and the community's declaration of June 1980. That called for recognition of the right of all Middle East states, including Israel, to live in peace and of the Palestinians to self-determination.

Saud said the kingdom was "very much interested that this initiative should maintain its independent position from the Camp David accords as well as its credibility."

"If joining . . . this multinational force means joining the process of Camp David, then there will be a contradiction between the European position and the position of the Arab world, which we hope is not the case," he warned.

In reply, Carrington sought to make a distinction between European participation in the Sinai peacekeeping force and Europe's backing of the Camp David accords.

He said that if the Common Market countries take part, as four -- Britain, Italy, France and the Netherlands -- are expected to do, it would be only on "the basis of seeing that Arab lands are returned to Arab countries and no other basis at all."