Later this week Prime Minister Menachem Begin travels to the United States to begin one of the most important and eagerly anticipated meetings ever held between an American President and an Israeli leader.

Begin is understood to be planning to try to persuade Carter that the best way to achieve a comprehensive Middle East agreement is to let the parties negotiate among themselves without either side being forced to make cancessions in advance of negotiations. Begin is also expected to try to persuade the President that he can, in fact, be reasonable and willing to make compromise.

It appears to be Begin's game plan to smoke out the Arabs and transfer the blame for intransigence from Israel to the Arabs. Begin apparently believes that the previous Israeli government badly lost the propaganda battle by always seeming to react negatively to Arab propaganda initiatives.

Personally, Begin comes across more like an old-fahioned schoolmaster than the popular image of an Israeli leader. He is more eloquent and far fluent in English than his predecessor, Yitzhak Rabin, and has more personal warmth.

The stakes are high. Although both Begin and Carter may believe in the desirability of a comprehensive Middle East peace settlement, longstanding policy differences between the United States and Israel have come to the fore and some important new ones have been added.

The Arabs and the Israelis have both said they are willing to reconvene a Geneva peace conference in the autumm, but there's still virtually no agreement on the three major elements - the nature of peace, the future borders of Israel and a homeland for the Palestinians.

There is an uneasiness and fear here that the American initiative for peace may already be faltering and that the tidal pull of events may soon begin to draw the region back towards confrontation, perhaps even war.

The Israelis fear that a major confrontation with the United States may develop. They fear that the imposition of an American peace plan will so limit their room to maneuver in any future negotiations as to make an agreement impossible. The Israelis disagree with the Americans who back to homeland for the Palestinians and a return to Israel's 1967 borders with only minor adjustments.

Begin and his closest advisers say, however, that they believe they can halt the deterioration in Israel's relations with the United States that has been evident for monthts.

"I leave for the shores of American with good hope in my heart," the prime minister said today. "On behalf of the government of Israel I shall offer a concrete proposal for the framework of a peace-making process," he added, "so that we can reconvene the Geneva conference starting the 10th of October." The prime minister said he was prepared to go into "specifics" with Carter.

Although the prime minister would not go into details before his meeting with the American President, sources close to him said that he will not present himself as a fire-breathing mystic who bases his politics on the divine right of Jews. The public statements that made Begin appear so hawkish to the outside world after his election in May have been carefully avoided since.

Begin is expected to try to persuade the American President that his public statements about going to Geneva without preconditions are sincere and that both sides should be allowed to present their maximum demands at the peace conference, at least as a starting position.

The prime minister fully believes in his ability to convince and persuade both the Americans and eventually the Arabs that his approach is correct.

Begin and his advisers indicate that they believe that the previous Israeli government made a great mistake in stating a willingness to concede specific territory in advance of negotiations. This, the new government says, simply encouraged the Arabs to make more demands.

The major problem between Begin and Carter will be Begin's consistent statements in public and private that the occupied West Bank should never be under anything but Israeli control. The contra-Begin is engaged in a semantic sleight of hand in which everything may be negotiable but the West Bank is not returnable.

Some of Begin's advisers, including Shmuel Katz, who recently toured America explaining the ruling Likud Party to worried Americans, say that if Begin were presented with a real peace settlement such as Carter recently described, with full recognition, exchanges of diplomats, commerce and so one, it mightbe that Begin would agree to compromise even on what he considers to be the sacred soil of Israel - just as Prime Minister David Ben-Gurion did when Israel was founded in 1948.

Begin might not even know himself what he would do if presented with such a deal but neither Begin nor the top men in his Cabinet profess to believe that the Arabs are ready to make a real peace with Israel. Thus the choice may not arise.

Begin has said he would be willing to go to Geneva without preconditions in October. Sadat has countered by welcoming the proposal. Never mind that there is no agreement on any of the basic issues - the rhetoric is meant to paint a picture of reasonableness.

Another example of the new Begin style seeking to transfer the label of intransigence came last week. "I suggest a political armistice." Begin said in a speech. "Let [The Arabs] be silent, then we shall be silent. If, however, President Sadat shall say, as he does say, that Israel, before we all meet in Geneva, should in advance give a commitment that it will retreat to the lines of June 4, 1967, otherwise he will not go to Geneva - then we shall tell him, if so, stay in Cairo."

Begin genuinely agrees with Carter that a comprehensive settlement is the best idea. Should that approach fail, then the new Israeli government is in agreement with the previous government that interim and partial agreements may be the answer. In this case, Foreign Minister Moshe Dayan would come into his own, for Dayan's opposition to giving up the West Bank is based more on security than on God's promise to the Jews.

Unlike the previous Israeli government, which appeared to lack leadership and direction, Begin has already demonstrated his ability to grasp power firmly and there is no question that he is the undisputed boss.

The new Israeli government also believes that the Carter administration tried at first to drive a wedge between American Jews and the new Likud government but that the attempt failed and, in Israel's view, backfired.

Begin is reading through reams of documents covering virutally every aspect and codicil of past negotiations and agreements. With his legalistic mind and phenomenal memory, he cannot fail to impress the Americans with his grasp of deail.

Begin remains a true believer - the description has become a cliche - and whatever personal rapport he may develop with Carter, there will remain great differences between them. A certain rigidity in Begin's game plan, despite its surface flexibility, may hinder the climate of mutual compromise that will be necessary if a reconvened Geneva conference is to be anything more than a propagenda forum.

In the past, the United States has recognized that to reconvene Geneva without achieving prior agreement on basic issues is to court failure. There is concern, given the wide gulf that exists between the Arabs and the Israelis, that the Carter administration has set its sights too high by asking for a comprehensive settlement in the Middle East and thereby risks missing the target altogether.