President Carter and Israeli Prime Minister Menachem Begin ended their two days of talks on Middle East peace yesterday in sharp and open disagreement on fundamental issues.

"Peace still seems far away," said a somber Carter in an unusually tense farewell exchange with Begin on the South Lawn of the White House. Members of the House International Relations Committee, whom he briefed later in the day, quoted Carter as saying that "the peace negotiations are at an end - I need your help."

Carter, in his meeting with the law-makers, and administration officials, in a briefing for reporters, made clear that the United States will continue its effort to arrange a comprehensive Middle East settlement. But there was no optimism.

A senior administration official called the Carter-Begin meetings "grim." Others indicated that the Carter administration has lost hope that Begin will show the flexibility they believe is essential for resumption of the momentum in the stalled Egyptian-Israeli talks.

The most basic difference between the two sides - as forecast in advance - was on Israeli withdrawn from the occupied West Bank. Carter privately and publicly reiterated the U.S. position that the withdrawal-for-peace bargain of U.N. Security Council Resolution 242 "must apply to all fronts if peace negotiations are to succeed."

Begin, on the other hand, stuck to his December negotiating offer of "self-rule" under continued military control for the West Bank, and quoted praise of it is as "positive constructive . . . forthcoming." U.S. officials confirmed that Begin does not accept U.N. Resolution 242 as requiring Israel to withdraw from the West Bank.

After his initial talks with Begin Tuesdday, Carter drew up a handwritten summary of the positions of the United States and Israel, he told House members, and it was clear to him in sum that Begin did not intend to withdraw from the West Bank. Carter said he had read his summary to assembled U.S. and Israeli officials in yesterday's White House talks.

Informed sources said Begin had been offered a variety of security arrangements including U.N. buffer zones, military cantonments a key points and formal U.S. guarantees, in an effort to make withdrawal from the West Bank in return for peace palatable on security grounds. The Israeli leader reportedly refused them all.

Major disagreement about Isreali settlements occupied areas was also reported. Officials who briefed reporters said Begin make no commitment to refrain from establishing new settlements in the West Bank, though they did say that no new settlements will be establisbed in the Sinai during negotiations with Egypt.

Egyptian President Anwar Sadat's peace initiative has been stalled on his demand for Israeli agreement in principle to withdraw from the West Bank. Sadat had been hoping that Carter would be able to convince Israel to change its position on the issue.

The White House meetings appeared to be a serious setback for U.S. relations with Israel as well as for Sadat's plans. Far from narrowing the gap between Washington and Jerusalem, the talks seem to have sharpened the disagreements and raised them to the highest levels of national leadership.

Standing with Begin at the departture ceremony, Carter reiterated U.S. support for "the security and the well-being" of Israel, and said that "We have stood beside Israel from the earliest moments of its birth, and there we shall continue to stand."

After that reassurance, however, the unsmiling Carter called his talks with Begin "detailed and frank" and said that he had informed him of "my assessment of what will be required to regain momentum in the common search for peace." Then he repeated the U.S. position that "all of the principles of Security Council Resolution 1242 must apply to all fronts if peace negotiations are to succeed."

Carter said that Begin faces "the challenge of providing security for his people, and the opportunity to achieve that security through a true and enduring peace." He added, "This opportunity must not be allowed to slip into the cycle of hatred and violence which has characterized the history of the Middle East for the past 30 years and which we have witnessed again over the past two weeks."

Begin, in turn, declared, "It is my duty as the elected prime minister of Israel to remind public opinion of the fact that Israel is still the only country in the world against which there is a written document to the effect that it must disappear." This was a reference to the charter of the Palestine Liberation Oragnization, adopted in 1968 and never rescinded.

Begin said Israel is threatened by an alignment of many Arab states, Union and sometimes getting modern "armed to the teeth by the Soviet weapons also from the West." He appeared to be referring to Carter's proposal to sell warplanes to Egypt and Saudi Arabia, which was defended anew by the president in the briefing for House members yesterday afternoon.

The Israeli leader said he had made "our contribution to the peace-making process" by proposing an Egyptian-Israeli deal in the Sinai and "full administrative autonomy" for Judea and Samaria (the Biblical names for the West Bank) as well as the Gaza strip.