In an atmosphere of developing political crisis, Israeli Prime Minister Menachem Begin withdrew to his house yesterday for several days of recuperation from "fatigue" and to work on a compromise solution to the division in his Cabinet over Israel's long-range plans for occupied Arab lands.

The Cabinet soul-searching over the future of the territories occupied in the 1967 six-day war - a debate which Deputy Prime Minister Yigael Yadin calls "an emergency situation that has no parallel since the establishment" of Israel - is expected to start formally again in a meeting on Sunday.

The 19-member Cabinet is spilt several ways over three proposed plans for the occupied territories, and Begin was said yesterday to be deeply troubled by his inability so far to reach a consensus on what Israel will do with the West Bank and Gaza after a proposed five-year limited self-rule plan for the Palestinian Arabs ends.

One of Israel's leading Hebrew newspapers, Haaretz, reported yesterday that Begin does not intend to bend on his insistence that the government not commit itself now to a discussion of the final status of the territories, and that if he is not supported by a majority of the Cabinet he may resign.

Aides to the prime minister said Begin has not talked about resignation, but they said he would have to reconsider his position if the debate goes against him.

The stalemate is over conflicting drafts of responses to two questions put to Foreign Minister Moshe Dayan last April by the U.S. State Department. The questions are whether a final settlement on the West Bank and Gaza issue will be possible after five years of limited Arab self-rule, and how the Palestinians will achieve a measure of political self-expression at the end of that time.

The protracted Cabinet debate has been interrupted several times, first because Israel sought to reassess its situation following the U.S. Senate's approval of the sale of warplanes to Egypt and Saudi Arabia, and later because Begin became ill.

The prime minister's health has become a recurring topic of discussion here, partly because of his near fatal heart attack last spring before his election. At times, Begin appears ashen and exhausted and close associates say that he occasionally loses his clarity of speech.

However, Israel government officials yesterday dismissed as unfounded a report that the prime minister had rejected the advice of his doctors to undergo a coronary bypass operation and they continued to insist that he is simply tired from a heavy work schedule and needs rest.

One Israeli official said that Begin may have been advised by a colleague to consider heart surgery, and that, characteristically, the prime minister would respond negatively, saying he feels well. However, officials stressed that Begin had received no recommendation by doctors that he undergo surgery.

The three draft responses to the questions posed by the United States have been submitted by Dayan, Defense Minister Ezer Weizman and Minister without Portfolio Chaim Landau.

Begin is said to be supporting the hardline proposal written by Landau, which sidesteps any mention of a "final" status for the occupied territories, and instead proposes that at the end of five years Israel will make up its mind about sovereignty on the basis of its experience in the trial period.

Weizman's plan is said to stress the importance of negotiating with the Arabs at all levels, while Dayan's proposal reportedly was to contain the notion that Israel's reply should be based on Israel's interpretation of Resolution 242, calling for withdrawal from occupied territories. Dayan is said to believe that his plan, which provides an active role for Jordan in the self-rule period, is compatible with Resolution 242.

Under all three plans, the Israeli army would remain in the occupied territories, a condition that has been rejected by the Arabs.

Cabinet sources say there are combinations and variations of the three draft proposals, and that if a consensus is not reached Sunday a "formulation committee" may be appointed, thereby further delaying the process.

The United States, Israeli sources say has signaled its unwillingness to accept vague and obscure language in Israel's response, because the answers will likely determine Egyptian President Anwar Sadat's course of action in his peace initiative begun in Jerusalem last year. If Israel's response is not explicit, diplomatic sources said, Sadat could abandon his bilateral peace initiative and return to the pan-Arab strategy in his dealings with Israel.

Cabinet sources said that at the moment, Weizman's draft response has a slight edge over the others, but that this could change before Sunday. Weizman met yesterday with Interior Minister Joseph Burg, of the National Religious Party, in an attempt to obtain a majority on the issue.

In another development, Israeli government sources said that U.S. Vice President Walter Mondale's visit here June 30, which officially is for recognition of Israel's founding 30 years ago, will include "substantive" discussions with Begin and Dayan on the stalled peace talks with Egypt.

Mondale's visit is being viewed by politicians here as essentially an attempt by the White House to rehabilitate its standing with the American Jewish community. But government officials stressed that the visit will not be regarded by them as an absolution of the Carter administration's F15 fighter sale to the Arabs and promises of new concessions in defense weapons purchases by Israel.