The Israeli Cabinet, in a demonstration of concern about U.S. intentions in the Middle East, decided today to dispatch Deputy Prime Minister Yigael Yadin on an urgent "political mission" to Washington.

Cabinet Secretary Aryeh Naor, who announced the 10-day trip, would not specify why it is being undertaken now, except to say that Yadin plans to leave Wednesday and will address "the [U.S.] government and public opinion."

The Cabinet decision, coming against a backdrop of strain in U.S.-Israeli relations over several controversial issues, nevertheless was interpreted widely as a sign that Prime Minister Menachem Begin and his government remain dissatisfied with explanations of what they see as a shift in U.S. policy on Israel and the Palestinians.

A report from Ephraim Evron, the Israeli ambassador to Washington, who met President Carter Wednesday for a discussion of the differences, was one of the main subjects reviewed during the four-hour Cabinet meeting, Naor siad.

Begin ran the meeting, the first he has attended since he was hospitalized three weeks ago for a minor stroke that has impaired his vision.

The prime minister emerged from the Cabinet session smiling and in apparent good health. He avoided waiting television cameras, however, and immediately was driven away.

Foreign Minister Moshe Dayan also attended despite being briefly hospitalized yesterday for treatment of a problem with his vocal cords. Dayan recently underwent an operation to remove a malignant tumor and said in an interview Friday that he views the possibility of death from cancer with tranquility.

Dayan's health was believed to have been a factor in the decision to send Yadin to Washington instead of the foreign minister. Dayan had planned a similar visit two weeks ago, however, to deal with a dispute on international observer forces in the Sinai. That trip was postponed because of a schedule conflict with discussions with Egypt.

In addition, Dayan caused a stir here Tuesday with two remarkably candid interviews in Israeli newspapers in which he accused the United States of tilting its foreign policy against Israel in response to pressure from wealthy Arab oil countries such as Saudi Arabia.

Sending him now to deal with the differences between Washington and Jerusalem could be viewed as inappropriate in the United States or as an official Cabinet endorsement of the views he expressed in the interviews. Moreover, several ministers are known to be upset with him for the frank talk, which also included bitter criticism of the Israeli government's economic policies.

Dayan, hoarse because of yesterday's treatment, joked with reporters that his doctors had ordered him to speak as little as possible and that he was unsure whether this was for medical or political reasons.

A number of Cabinet ministers are known to share Dayan's assessment of a shift in U.S. policy on Israel and the Palestinians, despite their discomfort at seeing him openly discuss the differences with Washington in such stark terms.

Naor said Begin ordered all his ministers to settle disputes among themselves in private or to come to him rahter than spread them across the pages of Israeli newspapers as did Dayan. This was seen as an attempt to demonstrate his authority and erase the growing impression here that members of the government find it difficult to work smoothly together.

Israelis have been complaining recently of sniping between ministers and a feeling of drift within the Cabinet. Dayan also referred to this impression in his interviews, saying the image of Israel abroad is inviting pressure from the United States on Middle East issues.

Israeli fears of a policy shift in Washington center on an Arab attempt to add a reference to Palestinian rights, including the right to a state, to U.N. Security Council Resolution 242, the basic U.N. formula for peace in the Middle East. U.S. diplomats are said to be cooperating in a search for an acceptable new resolution as part of a general review of Department spokesmen have reaftinians.

At the same time, however, State Department spokesmen have reaffirmed that there is no new policy, and President Carter recently repeated U.S. opposition to a Palestinian state.

The new U.N. resolution would be designed to encourage the Palestine Liberation Organization to accept Israel's right to exist within secure borders. This in turn could open the way for a U.S.-Palestinian dialogue, leading perhaps to increased Palestinian participation in autonomy negotiations between Egypt, Israel and the United States.

U.S. diplomats in the Middle East express little hope that Israel will change its steadfast refusal to deal with the PLO, which is regarded here as the reprehensible author of terrorist attacks on Israeli targets. But the diplomats say such open U.S. contacts with the PLO could result in a tacit approval from PLO leader Yasser Arafat for participation in the talks by leaders of the 1.1 million Palestinians in Gaza and on the West Bank.

Leaders of the area, who subscribe to the PLO stand, have so far refused to participate in the two-month-old negotiations.

In Israeli eyes, any tampering with Resolution 242 2ould alter the basis on which the March 26 treaty with Egypt was signed. Begin's government has dropped broad hints that it would reconsider its own participation in the autonomy talks if 242 is significantly altered or amended.

This stand, reportedly part of Yadin's brief for the Washington trip, reflects determination to keep the PLO entirely removed from the autonomy talks. PLO participation, or even participation by Palestinians who support the PLO, would bring Israel face to face with the Palestinian demand for a state in the West Bank and Gaza.

Israel resolutely opposes the idea of a Palestinian state in these territories, occupied since 1967, and envisages rather a tightly limited form of local administration of such needs as education, sanitation and health.

The Israeli concern about 242 underlines suspicions here that, despite assurances to the contrary, the United States is working to create through the autonomy talks a situation in which the Palestinians could move toward an independent state. The suspicions are heightened by a feeling that the United States has sided with Egypt in the autonomy talks so far and is cooperating with Egypt in maneuvering at U.N. headquarters over additions to Resolution 242. CAPTION: Picture 1, YIGAEL YADIN...chosen for "political mission"; Picture 2, Menachem Begin raises glass as staff toasts his recovery from mild stroke. AP