American strategists are anxiously looking to the leaders of Egypt and Israel to produce "imaginative responses" in private to exploit their unprecedented face-to-face exchange in Jerusalem yesterday.

The decisive test of a breakthrough in the Arab-Israeli struggle, specialists agree, is whether Egyptian President Anwar Sadat and Israeli Prime Minister Menahem Begin can build on their declarations for peace before Sadat leaves Israel.

Sadat and Begin set the stage psychologically yesterday for diplomacy to leap across a 30-year divide of hostility, specialists agreed. Their extraordinary debate in the Israeli parliament was candid, hopeful but - not too surprisingly - showed no shifts of public position.What is now critical is whether their private discussions can convert the spirit they evoked into new diplomatic momentum.

But the Sadat-Begin discussions also intensified debate in the United States about the American role in the diplomacy now evolving in Jerusalem.

Carter administration officials, from the President on down, yesterday hailed the Sadat-Begin talks and said they reinforced the administration's drive for a Geneva conference. For Geneva, the administration is championing a "comprehensive settlement" of the Arab-Israeli dispute, meaning peace agreements with Israel and all the Arab confrontation states.

Interviewed on television immediately after Sadat and Begin spoke, Philip C. Habib, under secretary of state for political that affairs, said Geneva "is a forum that is ready-made for this."

It is up to the parties to decide what diplomatic aid they want, Habib said on Face the Nation (CBS, WTOP), and the Carter administration will "wait for the visit to conclude" before it "decides what next step should be taken." But "the Geneva format is a flexible one" for any diplomacy ahead, he stressed.

Former Secretary of State Henry A. Kissinger, however, cautioned against any assumption by the United States about the diplomatic track to be employed.

"I think the United States at this point should not make any declarations of what it thinks a settlement ought to look like," Kissinger said in an either for a comprehensive or for a be either for a comprehensive or for a partial settlement."

If the Sadat-Begin talks succeed, Kissinger said, the United Stated "should take its lead from the participants." If the talks fail, Kissinger said, "then we will see a rapid worsening of the situation," and the United States "ought to look at it very carefully under those conditions."

Kissinger, who dominated U.S. strategy-making in Arab-Israeli diplomacy during the Nixon and Ford administrations, was making his most skeptical public remarks so far about a Geneva conference. U.S. officials noted yesterday, however, that both Sadat and Begin talked in terms of a Geneva conference with many Arab nations, rather than an Egyptian-Israeli peace settlement.

Kissinger said he believed Sadat's mission to Israel was a result of "his conviction that a Geneva conference that was prepared only in a procedural way was bound to lead to a deadlock" and would "leave no way out except and explosion."

A Geneva conference would include "the most radical elements" in the Arab world, Kissinger said, and "the Soviet Union, whose interests in the Middle East are not parallel to ours . . ." By contrast, Kissinger said, the Sadat-Begin talks are an occasion in history "where one symbolic act can change the course of events and where it's important for us not to lecture the parties on the details."

President Carter, after watching the Sadat-Begin speeches on television at the White House with his family, issued a statement calling them "a moving occasion and a contribution to the cause of peace.

Carter said the speeches were characterized by "candor and a spirit of conciliation. In that spirit we hope and believe it is possible to move towards lasting peace."

In order to watch the broadcast from the Israeli parliament, the President attended an early prayer session at First Baptist Church. There he stood in the pulpit, his eyes tightly closed, and said in prayer.

"Rarely has there been an opportunity in the history of mankind where the hearts and minds of all people could be attuned in thanksgiving and prayer.

"We are especially concerned about the Middle East. This morning we have a vivid realization that the chosen leaders have not responded adequately to this constant yearning, inspite of the yearning of the people of the Middle East for peace."

On leaving the church the President said, "I think that the fact that the Arabs, the Moslems, the Jews, the Christians all worship the same God, and freely acknowledge it, is a binding force" of achieving peace.

Landing Sadat's courage in going to Israel, Carter said in a brief ABC-TV interview that he was "particularly touched" on Saturday when he watched on television as Sadat walked down te receiving line on his arrival and "bent and kissed" former Israeli Prime Minister Golda Meir. "I thought that was a great occasion," Carter said: "I think it will be a great step forward."

Vice President Mondale, speaking before the Anti-Defamation League of B'nai B'rith at a luncheon, said a "seed for peace" was planted in the Middle East yesterday. "We are hopeful," he said, that the same spirit "will be carried through to negotiations at Geneva where all the parties can meet again as human beings face to face, in another historic encounter."

Secretary of State Cyrus R. Vance, in Puerto Rico enroute to Argentina on a South American tour, said Sadat's visit is contributing to "removal of the wall of mistrust . . . between Arab nations and Israel."

Senate Majority Leader Robert C. Byrd (D-W.Va.) said, "I hope the entire Arab world will support Sadat's courageous efforts to break the psychological barrier between Israel and the Arab countries."

Senior American officials said yesterday that they believe Sadat effectively dealt with a major initial hazard in his speech: staking out a position that would not allow moderate Arab nations to fault him for understating basic Arab demands on Israel, while not foreclosing the opportunity for bargaining with Israel.

It is not surprising, therefore, these officials said, that Sadat repeated basic Arab terms for a settlement without adding anything new. What was significant, these sources said, was Sadat's eloquence in specifically acknowledging what years of hostility have done to Arab and Israeli perceptions of each other.

Begin's speech, these sources said, was probably most significant in what it omitted: he avoided harsh, unyielding language on retention of war-occupied territory.

As Kissinger noted, however, each speaker inevitably was primarily addressing "his own audience" in yesterday's public remarks.

While Sadat and Begin now continue their more diplomatically important provate talks, world reaction will be rebounding against the public speeches. Here Sadat is the more exposed, to radical Arab country.

The Carter administration privately has told the Soviet Union that it is quite displeased with Soviet support of radical Arab attacks on Sadat, in contradiction to the joint U.S.-Soviet pledge of Oct. 1 to encourage peace talks at Geneva.

Carter is reported to have expressed that displeasure to Soviet Ambassador Anatoliy F. Dobrynin when they talked briefly on Friday. The State Department's Habib said yesterday, "We're not particularly pleased with the criticisms of he Sadatmission that have been put forth by the Soviet Union." He said the United States intends "to play a responsible role."

Kissinger said he has high hopes for the Sadat-Begin talks, but "if this visit fails Sadat's position in the Arab world can be salvaged only by his taking an extremely radical course."

Equally Kissinger said, "If this visit fails, Israel will go back into isolation and the tendency toward radicalization of the whole situation will accelerate."