The White House yesterday released the first of the letters of understanding agreed to at the Camp David summit as U.S. officials continued to predict there will be a resolution of the dispute with israel over new settlements on the West Bank of the Jordan River.

Egyptian President Anwar Sadat, in a letter to President Carter, said that Egypt is willing to "assume the Arab role" in negotiations over the West Bank and Gaza if Jordan, which controlled the West Bank until the 1967 Arab-Israeli war, refuses to participate.

In other letters released yesterday, Sadat and Israeli Prime Minister Menachem Begin expressed sharply different views on Jerusalem, and Sadat warned that if lsrael does not agree to withdraw its settlements from the Sinai peninsula the "framework" for an Egyptian-Israeli peace treaty "shall be void and invalid."

In all, the White House released nine letters that have been exchanged among the three leaders who met for 13 days at Camp David. Md., and produced two "frameworks" - one for an Israeli military withdrawal from the occupied Sinai and one for a five-year transitional period during which the status of the Israeli-occupied West Bank and Gaza territories would be negotiated and decided.

But the letters made public yesterday did not include those dealing with the most volatile issue to arise since the end of the summit conference: the question of future israeli settlements on the West Bank.

American officials insist that at Camp David. Begin agreed to a lengthy moratorium on new Jewish settlements on the West Bank by accepting a formula that would, in effect, give Arab negotiators a veto over the establishment of new settlements during the five-year transition period.

Begin has said he agreed to no such thing. In an interview Thursday, he expressed displeasure with the decision of White House officials to show reporters handwritten notations by Carter on a Camp David summit document supporting the American contention.

It was learned yesterday that the White House has sought to soothe Begin's anger. On Thursday, Hamilton Jordan, the president's chief political adviser, visited Israeli officials traveling with Begin in New York to offer an explanation of why the White House showed the document to reporters.

Negotiations are still going on over the language of letters dealing with the West Bank settlements.

An American official, who refused to be identified, said yesterday there are "still problems in finding the precise language to express what we still think is an agreement."

He added, "I am quite confident the right language will be found . . . We expect to have a common point of view. We do not believe there is a substantial difference [between Israel and the United States] on this point."

Sadat's offer to "assume the Arab role" in the West Bank and Gaza negotiations raised the possibility that the negotiations could go on even if Jordan, which is now being pressed by the United States to accept the Camp David "framework," refuses to join. Sadat has said he would negotiate on the status of Gaza, controlled by Egypt until 1967, and apply the terms of a Gaza settlement to the West Bank.

In the dispute over Jerusalem, Begin and Sadat agreed that the city should be "undivided." Sadat proposed creation of an Arab-Israeli joint municipal council, but insisted that Arab Jerusalem (East Jerusalem) "should be under Arab sovereignty."

Begin, in his letter, cited a section of Israeli law stating thay "Jerusalem is one city individsible, the capital of the state of Israel."

Setting out the U.S. position. Carter, in his letter, cited two previous statements made by the United States at the United Nations. One of them, by Ambassador Arthur J. Goldberg, on July 14, 1967, asserted that the status of Jerusalem cannot be decided by "unilateral actions" and that the Israeli annexation of East jerusalem in 1967 "cannot be considered other than interim and provisional."

The letters released yesterday also dealt with the agreement on Israeli settlements in the Sinai. Begin pledged to bring to a vote in the Israeli Knesset in the next two weeks the issue of withdrawal of the settlements provided other terms of peace treaty with Egypt are reached. Sadat has said a favorable Knesset vote is a prerequisite to the begining of peace negotiations.

Still to be released are letters dealing with a U.S. pledge to build two military airfields for Israel to replace three airfields in the Sinai to be turned over to Egyptian civilian control.