Beneath the Moorish arches of a converted hotel dining room, representatives of Israel and Egypt today began tentative, groping negotiations toward ending the hostility that has inflamed the Middle East for 30 years.

The opening session of their talks was brief and formal. By prearrangement, nothing of substance was discussed. The opening remarks by the heads of their delegations showed that they remain far apart in their approach to the negotiating process.

But both proclaimed their desire to reach a comprehensive agreement that would mean peace not only for them but for Israel's other Arab neighbors as well.

Four delegations attended the first session of this historic conference called by Egyptian President Anwar Sadat. They represented Israel, Egypt, the United States and the United Nations. There were five empty chairs around the big round table in a symbolic reminder that five other refused to attend - Syria, Jordan, Lebanon, the Soviet Union and the Palestine Liberation Organization - although for a while the flats of all nine flew together outside the Mena House Oberoi Hotel.

The conference, to which Sadat issued the invitations after his visit to Israel that transformed the atmosphere of the entire Middle East, is officially described as an informal gathering of "experts." Their purpose is to settle the "procedural obstacles" in the way of a full-scale peace conference at Geneva. It is in fact so informal that there is not yet any agenda or timetable, and the delegates admitted they were groping their way in the absence of any clearly defined program.

The fundamental differences in approaches were evident in the public pronouncements. The Israelis were interested in the nature of peace before they make territorial and other concessions. The Egyptians were pressing for territorial withdrawal and the discussion of the Palestinian question.

Yet the first meetings were so amicable that the Egyptian and Israeli delegates were reportedly calling each other by their first names. It was a case, one Israeli said, of Jews and Moslems calling each other by their Christian names.

It appeared this morning that this conference, despite its symbolic importance, might become a mere side-show to the surprise trip to Washington of Israeli Prime Minister Menahem Begin.

Authoritative sources within the delegations said, however, that Begin's trip and his planned meeting with President Carter were being treated here as a useful supplement to the Cairo talks and as a bilateral arrangement between the United States and Israel, not as an attempt to circumvent this conference.

The chief U.S. delegate. Assistant Secretary of State Alfred Atherton, told reporters that whatever happens on the Begin visit, there is "a lot of groundwork to be done" here in Cairo and "we can proceed as if Begin were not in Washington." Atherton said the objective was to strive for a "meeting of the minds" between Egypt and Israel over procedural obstacles to substantive negotiations.

Begin sent a message to Fliahu Ben Uissar, head of the Israeli delegation, saying that "people everywhere hope and pray that Cairo will be a foundation for true democracy between Israel and its Arab neighbors. The peace which is necessary for Israel and her great Arab neighbors."

Egyptian officials have been saying that they expected consultations and initiatives in different forums and at different levels, now that the initial breakthrough has been made, so the Begin trip came as no surprise to them. Sadat was notified of it in advance, informed sources said.

The Israelis say it is a separate matter and the authority and instructions of their delegation here have not changed.

That authority is apparently limited. An American official said after the first meeting today that "no delegation here has the authority to negotiate policy," and it remains unclear just what they are authorized to do.

Israeli and Egyptian officials, as well as the Americans, stressed that the atmosphere is good, the attitude constructive, and the negotiators flexible. But as one delegate put it, "no one has any illusions that this is going to be easy. They all know it will be difficult."

A hint of how difficult could be found in the opening speeches by the heads of the delegations, which were televised. As expexcted, they showed that Israel and Egypt still have very different ideas about how to proceed, what issues should be tackled first, and what the obligations of their respective countries are.

The chief Egyptian delegation, Esmat Abdel Meguid, said that the whole world "earnestly hopes that Egypt's genuine desire to establish a just and lasting peace be reciprocated by the government of Israel. Tangible and concrete results are expected and should be forthcoming without delay."

He said Egypt wanted quick movement toward a comprehensive settlement, not a bilateral one, that would be based on the principle of the U.N. Charer and and would realize "the legitimate rights of the Palestinian people."

Ben Elissar told the gathering that while their flight from Israel yesterday was brief, "the journey of the spirit was infinite." He expressed his gratitude to Egypt for the invitation and recalled the milennia in which, he said, the two states have been linked by geography and history.

Israel wants peace with all her neighbors, he said, and wants it on the basis of these elements: termination of the state of war forever; establishment of diplomatic relations; commerce; international cooperation; use of international waterways; mutual assistance in all fields of national activity.

"It is proper that these goals be achieved at a reconvened Geneva conference," he said.

Thus they made clear in public what already known from informal contacts and from background conversations - Israel wants first to talk about the nature of peace and the kind of receptions it will get from the Arabs if it yields any of the territories occupied in the 1967 war; the Egyptians want to start with the principle of withdrawal and the recognition of the Palestinians.

In the middle is the United States, to which both both sides are looking as broker and supporter. Atherton said in his opening remarks that the Americans are "ready to do whatever we can to facilitiate, support and encourage the negotiations here to prepare the way for the Geneva Middle East peace conference and the achievement of a comprehensive, just and durable peace in the Middle East."

He praised Sadat and Begin for bold statesmanship that has created "unique opportunity" to negotiate peace. He said the United States is "fully dedicated" to help them, although "we can expect moments of discouragement."

Other American officials said Atherton had not been sent here with any negotiating initiatives or proposals for peace. The United States, they said, is here essentially as ago-between.

All three said they regarded U.N. Security Council Resolution 242, adopted after the 1967 war, as the basis for peace negotiations. Delegates acknowledged, however, that the diplomatic beauty of that resolution is also its greatest deficiency - it is deliberately ambiguous so that all can espouse it while disagreeing on what it really means.

It calls for withdrawal from occupied territories but the Egyptians say that means all territories and the Iraelis do not. The resolution of that fundamental difference is not yet at hand.

The heads of the delegations expressed regrets at the absence of those who elected to stay away. Even Ben Elissar said Israel would have been willing to talk to "an appropriate delegation of Palestinian Arabs," although not to the Palestine Liberation Organization. Chairs for the absentees are expected to be removed at the closed sessions beginning Thursday as there is now no hope of their attending, officials said.

Rarely has an international conference been so unstructed. There appears to be broad agreeement that the delegates will tackle procedural problems such as whether, at Geneva, all participants should discuss all matters or the work shoudl be parcelled out to committees. By tonight, however, there was still no agenda, no timetable, no agreement on days off and no decision on duration. After the first clared meeting, the delegates held a two-hour informal session to try to iron out agenda problems, an Israeli spokesman said.

The Egyptians hosted the Israelis at dinner but the only other certainty appeared to be that the Israelis have accepted an invitation to take a sight-seeing tour.