Upset by the decision of White House officials to challenge his word in public, Israeli Prime Minister Menachem Begin asserted yesterday that he has written proof that he did not give President Carter a promise for a lengthy moratorium on Jewish settlements on the West Bank.

"I didn't agree to that," Begin said in an interview here. "My reaction was, I will consider it and I will write to" President Carter about a U.S. proposal for a negotiating framework that would give local Palestinians an effective veto over future Israeli settlements.

"If I had accepted it, I would have said so." Begin stated. Israeli notes of the discussion have been checked and support his view, he said. Asked about the display to reporters in Atlantic City Wednesday of Carter's handwritten notation of the disputed clause, Begin replied, "Let me respectfully say that they shouldn't have done that . . . it is not proper to show to the media texts that have not been approved."

With the White House insisting yesterday that agreement had been reached at the Camp David summit, the dispute continued to block the scheduled exchange of a letter that is supposed to spell out an agreement on future Israeli settlements in the West Bank and Gaza Strip territories.

But Begin disclosed that despite the dispute, Israel, Egypt and the United States exchanged two other letters of understanding yesterday growing out of the 13-day Camp David summit on the Middle East. Moreover, he was insistently optimistic that he and Egyptian President Anwar Sadat will shortly sign a binding peace treaty, no matter what transpires in the complex arrangements drawn up at Camp David for the West Bank and Gaza.

"Everything is agreed upon, with contents and dates. As far as Egypt and Israel are concerned, we almost have a peace treaty. Except for the one issue [of Israeli settlements in the Sinai] we could sign the treaty today," Begin said.

But he predicted that a vote by the Israeli Knesset on Sadat's demand that the Israeli settlements in the Sinai be dismantled as a prerequisite for the signing of the peace treaty would be extremely close and "might be decided by one vote, or two votes, or three votes."

Begin, Carter and Sadat concluded the summit last Sunday night by signing two agreements, one called a "framework" for an Egyptian-Israeli peace treaty and the other called a framework for negotiations over the "final status" of the Israeli-occupied West Bank and Gaza Strip.

Making other points in an interview conducted by The Washington Post and Newsweek magazine, the Israeli prime minister said:

He will resign if the Knesset votes on Monday against the two framework agreements. But Begin said he believes "there will be an overwhelming majority" in favor of the two accords.

If a separate vote he has scheduled for a week later on the Sinai settlements "should go against my conviction, I will not resign. I will abide by any decision of the majority" on this question, which Begin indicated was of less fundamental importance than the two framework accords. He again declined to say how he would vote on the issue.

While he is not deliberately leaving the difficult question of the 1983 decision on the final status of the West Bank and the Gaza Strip for a successor to handle, it is likely he will have left office by then. "I want to leave politics completely by the time I am 70," he said, adding, "I am now 65."

If elections produce a self-governing authority that includes' residents of the West Bank and Gaza Strip who are supporters of the Palestine Liberation Organization, the Israelis will negotiate with them. "It may happen. We will have to take that risk," he said, adding that the Israelis would demand that the Palestinians "not disturb the peace."

If the full autonomy plan and four-sided negotiations on the status of the West Bank and Gaza fail to produce a decision acceptable to Israel, the Israelis will simply maintain the status quo of occupation. "Nothing wrong will happen. Autonomy will continue."

Israel feels Carter gave a clear commitment to support Begin's vow that Israeli troops will remain on the West Bank after the five-year interim period ends, whatever decision is reached on the territory's final status. Begin said the Carter gave that commitment by agreeing to include in the agreement a stipulation that "all necessary measures will be taken" to assure Israel's security "during the transitional period and beyond," U.S. officials thus far have not disputed this view.

Carter was told by Begin during the summit that while Israel did not want U.S. troops stationed in the area, it would agree to the setting up of American military facilities and bases in Israel if the United States wanted them for global security reasons. He specified that this included the possibility of establishing an American base in Israeli-held portions of the Sinai peninsula during the three years Israel has to return all of Sinai to Egypt, but he stressed that this would have to be done at U.S. initative.

The interview was conducted a few hours before Begin left New York for home, after a busy day of receiving visitors in his stately East Side hotel suite. Hamilton Jordan, President Carter's chief political adviser, was also at the hotel yesterday.

Jordan told reporters that he was there "by coincidence," but it was established that he paid a call on the Israeli ambassador to the United States, Simcha Dinitz. Dinitz said Jordan's visit was courtesy call.

The prime minister had engaged in an intensive schedule of television appearances, private meetings and a major speech since concluding the 13-day summit. He showed signs of fatigue as he sat in an armchiar and talked quietly for nearly one hour. But he appeared to be in good spirits.

The letters exchanged yesterday cover the three delegations' sharply conflicting views on Jerusalem, which Begin says will always remain unified and Jewish, and the prime minister's use of the Biblical terms Judea and Samaria. Carter has written Begin saying the U.S. understands him to mean the West Bank.

A set of 10 letters dealing with topics on which the three sides did not have the same views was due to be exchanged within a day or two of Sunday's ceremony. The procedures agreed upon to resolve the Sinai settlement question are covered in one letter, with Egypt reportedly saying that the entire Camp David accord collapses if the settlements question is not resolved.

It is not clear, however, that the Egyptians view the West Bank settlements issue seriously enough to back away from their own agreement with Israel should the dispute block the exchange of the West Bank letter. Egyptian Ambassador Ashraf Ghorbal declined for the second consecutive day to return a reporter's calls on this question.

Rather, Sadat appears to be letting the United States argue the Arab case in this dispute, a role he has repeatedly sought to press on Washington. U.S. officials let it be known to reporters that Secretary of State Cyrus R. Vance had emphasied the firm American stand on this in his meeting with Jordan's King Hussein in Amman.