The collapse of U.S.-nurtured peace prospects in the Middle East - a growing possibility in the light of new statements by Israel's election winner - would be a foreign for President Carter and could seriously strain U.S. relations with both Israel and the Arab world.

Menahein Begin, leader of the rightist [WORD ILLEGIBLE] Party, which won Tuesday's election, said in an interview on NBC's "Today" program that territory occupied in the 1967 war is "our land" which should be formally incorporated into Israel. In a later speech in the occupied area he called it "the land of liberated Israel" and promised many future Jewish settlements there.

An Israeli policy determination not to withdraw from major portions of the territory taken in 1967 would appear to doom the chances for a Middle East settlement along the lines suggested by Cartr during the past three months. And because of Carter's commitment of time and prestige to the peace process in meetings with Israeli and Arab leaders, a dramatic failure could have dramatic repercussions.

Despite an announced agreement yesterday by Secretary of State Cyrus R. Vance and Soviet Foreign Minister Andrei Gromyko to press ahead toward a Geneva peace conference this fall, specialists here doubt that such a conference will be posble under a Begin government.

About the best they hope for, under the circumstances, is a postponement of Geneva for some months until Begin changes his policies or is ousted in new elections. The danger is that, even if this should happen, the interruption could be fatal to the dipomatic momentum for a peace agreement.

The improved relations between the United States and Arab nations following the 1973 Middle East war and oil embargo were built on the explicit U.S. promise to seek a settlement in the region and the Arab belief the the United States could deliver because of its influence with the Israelis.

The shattering of the Middle East peace effort could therefore undermine U.S. relations with Arab governments. The loss of confidence could also threaten the stability of moderate Arab leaders, such as Egypt's President Anwar Sadat, who have aligned their policies to the United States.

Washington's stake in the Arab world will be dramtized by the official visit here next week of Saudi Arabia's Crown Prince Fahd, who is to discuss Middle East peace prospects with Carter. Saudi Arabia is now the leading supplier of petroleum to the United States, providing more than 20 per cent of crude oil imports, and is the main hope for the expanded imports to fuel the U.S. economy in the next few years.

Fahd, Sadat and Syria's President Hafez Assad were meeting yesterday in the Saudi capital of Riyadh. A Cairo Radio said the three leaders discussed the Israeli election results and "a common Arab stand should there be any changes in the Middle East situation." No details were given.

The "special relationship" between the United States and Israel - reaffirmed only yesterday by Carter in announcing his arms export policies - is likely to be strained more than ever before if the Jewish state rules out the territorial and other compromises which are at the heart of a potential settlement.

Since 1973, Israel has become financially dependent on the U.S. official aid to a greater degree than ever before - but on the premise that this aid helps to assure Israel's willingness and ability to seek peace.

Speaking of Israeli and Arab aid - which make up the lion's share of U.S. military and security assistance - the House International Relations Subcommittee on the Middle East recently noted that "in the absence of further memontum toward peace, these, large figures will be increasingly questioned in Congress."

The strong support for Israel in the American Jewish community, underlying Israel's political strength in the American political system, could well be threatened by Begin's policies and their diplomatic-military consequences. Some U.S. Jewish leaders are reported to have started sending private appeals to Begin to keep in mind the opinions of American Jews while formulating his stance.

So far there is not much sign that Begin is prepared to change his longstanding insistence that the occupied territories are "our land" which must not be given up. The existing Labor Party government has demanded "defensible borders," but it was not opposed on principle to territorial compromise, and was thought to be prepared to deal at the right moment.

Official and private experts here pointed out that Begin's success in forming a government is uncertain and his future policies are not definite. Nevertheless, his tough words have cast gloom over the search for an Arab-Israeli settlement.