Prime Minister Menahem Begin said yesterday that Israel is offering "automony, self-rule" to Palestinian Arabs on the West Bank of the Jordan River, with a "mutual right of settlement" and "security" there for Palestinian Jews.

This alternative to Arab demands for a Palestinian state would permit Palestinian Arabs to have a genuine self-rule "for the first time in history," Begin contended.

Interviewed on "Face the Nation" (CBS, WTOP), Begin gave the first official description of the proposals that he outlined to President Carter and will bargain out with Egyptian President Anwar Sadat. While avoiding details until he meets with Sadat later this week or early the following week, Begin said:

"We shall live together in Judea, in Samaria [biblical terms for the West Bank area] and in the Gaza district" with a "mutual right of settlement" of "Jews and Arabs alike in all parts of the land." It "will be the right of the Arabs in Judea and Samaria to settle in Israel" with "symmetric justice" and "free movement."

This West Bank-Gaza issue, rather than return of Egyptian sovereignty over the Sinai peninsula, dominated his discussions with Carter (Israel is reportedly prepared to restore Egyptian sovereignty in the Sinai, while reserving or leasing limited security areas).

Israel is determined that Jerusalem will remain "one city," with "completely free access to all the holy shrines" of all religions. Begin said there will perhaps be "a proposal about self-rule of the religious representatives of their holy shrine . . ." (the Arabs have demanded an independent East Jerusalem).

He sought and obtained "the good will" of the United States for Israel's proposals, did not ask Carter for "any commitment," and is leaving Washington "a happy man." With "very complicated problems to solve . . . the American endorsement couldn't be complete" at this stage.

If agreement is reached with Egypt, Begin will suggest that Carter invite him and Sadat to Washington, so that a Christian President, a Moslem President and a Jewish Prime Minister can "announce to the world Pax Vobiscum, Salaam Aleikun, Sholom Aleichem" - "Peace be with you" in Latin, Arabic and Hebrew.

It is up to the United States, if it desires, to propose an American-Israeli mutual security pact, as a separate matter. But Israel does not need, seek or trust its fate to international security guarantees. And neither he nor Sadat wants "the Russians in our region at all."

Begin said the Israeli objective is not in Egyptian accord alone but rather an Arab-Israeli "comprehensive peace settlement." Begin previously has said, even after Sadat's dramatic visit to Jerusalem last month, that Israel would be willing to start with an Egyptian-Israeli accord but that Sadat wants a wider agreement. In either case, the starting point presumably will be an Egyptian-Israeli settlement.

Begin made no reference yesterday to another reported ingredient of the proposed West Bank-Gaza Strip settlement - a link between that intended autonomous region" and Jordan. He noted that Jordan, Lebanon and Syria are not participating in the current Cairo peace talks but expressed hope that they will join the negotiating process later.

Also, Begin did not amplify on the security rights that Israel seeks to retain in the West Bank and in the former Egyptian-occupied Gaza Strip. Nor did he mention that Israel reportedly intends that no nation will have sovereignty over this double autonomous region. It is premature, he said, to disclose details prior to his next meeting with Sadat.

Begin projected his West Bank-Gaza Strip concept as a major Israel concession. The Arab demands, however, have been for outright return of all war-occupied territory. The Carter administration's position has been that Israel should return all territory except for minor border adjustments.

When Begin and Carter concluded their talks Saturday night, Secretary of State Cyrus R. Vance said Carter welcomes Begin's "constructive approach" and "the understanding and statesmanship" he is demonstrating.

That endorsement stopped short, however, of stamping outright support on Begin's specific proposals. A White House official said what Begin presented represents a step forward in a process that requires considerable work to reach an agreement, and it would be premature and unwise for the United States to say more at this time.

Begin said yesterday that he is quite content with this, and that Carter "considers the proposals I brought to him a fair basis for negotiation to achieve peace."

A statement issued in Tel Aviv yesterday by Israeli Cabinet Secretary Arieh Naor went beyond what either Begin or Carter have said. "For the first time since the establishment of the state" of Israel in 1948. Naor said, "we have an indentity of views on the content of a peace agreement."

Begin said in yesterday's television interview that "we brought ideas which will give the Palestinians Arabs autonomy, self-rule, and the Palestinian Jews security." There are about a million Arabs in the Bank-Gaza region.

Referring to the West Bank Arabs, Begin said they "were ruled for centuries by the Turks, for decades by the British, for nearly 20 years by the Jordanians, and for the last 11 years by military government of Israel." He said "the latest rule was the most benevolent," but "military should defend people, not govern people."

Under the Israeli plan, he said, two areas "will have the possibility to conduct their own affairs through their own elected men." Asked if they could elect Yasser Arafat, leader of the Palestine Liberation Organization, which Begin scorns as a group bent on destruction of the Israeli state, Begin said he cannot believe that those who have "a completely negative attitude, a destructive attitude" would be candidates or would be elected.

When asked if the Israeli plan would continue "in perpetuity." Begin said, "There can always be a review," but he again declined to go into details.

Begin's disclosure of his idea for a Carter-Begin-Sadat summit meeting in Washington to confirm an agreement caused a questioner to ask if the objective was "to have a little theater, historic theater?" Begin bristled at the characterization, saying he saw nothing "theatrical" about "a very serious event in the annals of the Mideastern nations and all the nations." Asked why they should meet in Washington, Begin responded, "Because President Carter contributed very much to this process," but he said Carter and Sadat may have "other ideas" about such a meeting.

As for an American-Israeli security pact, Begin said he and Carter did not discuss that, but if the United States suggests it, "we shall consider it very seriously, and positively . . ." But "it may embarrass the United States" to raise that now, he said.

By contrast, Begin's expressed lack of interest in "international guarantees" conformed with his previous view that in the past such gurantees have proved worthless, for Israel and other nations.

As Begin left Washington yesterday for New York, and a stopover in Britain Tuesday before returning to Israel, the timing of his next meeting with Sadat was uncertain.

Begin said they "may meet either at the end of this week or the beginning of next week."

Sources at the Cairo conference, which includes Egypt, Israel, the United States and a United Nations observer, said the Begin-Sadat meeting could be delayed for "organizational and medical" reasons. This was an allusion to the physical strain on Begin, who has a heart condition.

It was suggested in Cairo that the meeting could take place on Christmas Day, or immediately afterward. An Israeli newspaper, however, said the Egyptian government would prefer to postpone the meeting until early January, if Begin is unable to go to Egypt this week.