President Carter today tried to assure Israel and the Arabs that the United States is fairly defending their mutual "right to exist in peace," but Israeli suspicions remain high over the new coordination of American and Soviet policy.

"We do not intend to impose, from the outside, a settlement on the nations of the Middle East," Carter said in trying to assuage Israeli alarm that the United States has undercut its interest. Carter told the overwhelmingly pro-Arab forum of the U.N. General Assembly that "the Commitment of the United States to Israel's security is unquestionable."

At the same time, Carter personally embraced the language in last Saturday's U.S.-Soviet statement that has aroused dismay in Jerusalem. "For the Arabs, the legitimate rights of the Palestinian people must be recognized," he said.

To Israel and the Arabs that is code language for movement toward a separate Palestinian entity or state. Carter, however, sought to equate its meaning with "human rights" and also with "the rights of all peoples in the area." He said that how "these rights are to be defined and implemented" is "not for us to dictate," but "for the interested parties to decide in detailed negotiations."

Congressional sources said in Washington that the White House had provided a detailed informal report to House members friendly to Israel justifying the Saturday statement as the most that could be obtained from the Soviets and certainly not an abandonment of U.S. support for Israel.

Carter's most challenging task in his two days in New York is to keep Israel from abandoning the American- Soviet-Arab drive for a Geneva conference this year that would include Palestine Arabs.

As Carter met tonight with Israeli Foreign Minister Moshe Dayan, the prospects for the American objective were clouded.

Carter's meeting with Dayan was moved up a day so it would be the same day that Carter met with Egyptian Foreign Minister Ismail Fahmi.

Egyptian sources said that Fahmi, in an hour's meeting with Carter, delivered a private message from President Anwar Sadat commending Carter for the first endorsement of Palestinian "rights" in the American-Soviet statement. Sadat, the sources said, also thanked Carter for saying last Thursday that the Palestine Liberation Organization - with which Israel refuses to negotiate - represents "a substantial part of the Palestinians."

American officials describe the Fahmi-Carter talks as "constructive, with indications of progress" toward a Geneva conference.The focus of attention here tonight, however, was Carter's meeting with Dayan.

After listening to Carter's address to the United Nations, the Israeli minister said cooly. "We will be seeking some clarification in what was said in the Russian, and in what he said in his speech." Dayan's acid reference to "the Russian" was a wry allusion to the American-Soviet declaration, which began as a Russian initiative, and employed some Soviet-style phraseology in the document that emerged from the U.S.-Soviet barganing.

Another illustration of the mood on the Israeli side came from Chaim Herzog, head of Israel's permanent delegation to the United Nations. After hearing the President, Herzog said: "There is a very big issue here, and that is the credibility of American undertakings."

"When we have clear, specific, written undertakings of the United States government . . . the joint U.S.-Soviet statement was in my view an erosion of that commitment," he said.

Herzog was referring to the American pledge in 1975 that gave Israel virtually a veto over any U.S. agreement to change U.S. resolutions that would be the basis for reconvening a Geneva conference. U.S. officials insist that the Carter administration has honored that pledge; Israel claims that at least its spirit has been undermined and protested the omission of references to those resolutions in the American-Soviet statement.

"It was gratifying" to hear Carter refer to those U.N. resolutions today, Herzog said, but he added, "What is still disturbing is the background of the American-Soviet statement, which brings the Soviet Union, in our view prematurely, back into the Middle East, remembering that they have no bilateral relations with us and they therefore cannot be honest brokers."

The Carter administration's attitude toward Israel now, as in the presidential election campaign, was described today as "we will not deceive, we will not betray, we will not compel." That was said today by a senior White House official, as White House background rules required reporters to identify the speaker. At a subsequent press conference however, White House press secretary Jody Powell unintentionally identified the speaker as presidential national security advisor Zbigniew Brzezinski.

Brzezinski told reporters that he saw nothing "inconsistent" between the President's denials today of any attempt "to impose" a peace settlement in the Middle East, and Brzezinski's own comments in a recent interview in which Brzezinski had said that the United States has "a legitimate right to exercise its own leverage" to obtain a Middle East settlement.

The United States and Israel, Brzezinski said today, have the deepest of ties, but also some differences. He said, "I don't thing that one should overreact when some of those differences surface, as they are bound to surface in a difficult process of seeking a settlement."

Carter told the United Nations that "Israel and the Arab countries have a right to exist in peace, with early establishment of economic and cultural exchange and of normal diplomatic relations."