Amid signs of continued wide disagreement over the means of moving toward a comprehensive Middle East peace, Israeli Prime Minister Menachem Begin and Egyptian President Anwar Sadat began a new round of talks here tonight to explore the prospects of breathing new life into the stalled Camp David peace process.

As the talks began at a pre-dinner meeting at President Sadat's Maamora Palace by the Mediterranean Sea, Israeli and Egyptian officials were clearly lacking in agreement on just what this new two-day summit -- Begin and Sadat's 11th since the Egyptian president flew to Jerusalem in 1977 -- would seek to accomplish.

Conference sources said that little was expected to be resolved by the meetings. Some suggested that Begin, who after his recent reelection has formed a government that has stiffened Israel's position on the future of its occupied territory, is interested in showing the Reagan administration that he wants peace with Sadat, who recently returned from a trip to Washington.

Begin is scheduled to visit Washington next month, and is said to be highly concerned about his reception.

Israeli Foreign Ministry officials have said that Begin hoped to press Sadat hard for a full-scale normalization of their relations and a resumption of the West Bank and Gaza strip autonomy talks that Sadat broke off a year ago after the Israeli Knesset officially annexed East Jerusalem and proclaimed it part of the "eternal capital of Israel."

Israeli officials clearly fear that if agreement is not reached on normalization by April, when the withdrawal of Israeli troops from the Sinai is complete, it may never come about. The worry is that once the withdrawal is finished, the leverage on Sadat that the occupation has allowed Israel will be removed.

The Israelis are irked by the slowness with which Egypt has allowed tourist, cultural and commercial exchanges to develop since the Camp David peace treaty was signed. Egyptian-Israeli trade is running at a lopsided imbalance -- Egypt's trade payments from Israel amount to about $550 million dollars, compared to the $12 million Israel receives -- and the imbalance in tourism is equally great.

For their part, Egyptian foreign ministry officials have insisted that Sadat will urge Begin at this summit to first establish "confidence-building" measures in the occupied territories and bring Palestinians into the talks before the autonomy discussions resume.

President Sadat is also committed to renewing the appeal he made in Washington that Israel and the Palestine Liberation Organization (PLO) agree to some form of mutual recognition. Since such a proposal has already been denounced by Begin, however, he is not expected to push it.

Despite the clear divergence of their pre-summit positions, the talks got off to a cordial, if restrained start five hours after Begin flew from Israel to Alexandria's Al-Nozah airfield.

The summit proper began at 6:30 p.m., when Begin arrived at the Maamora Palace and the two leaders moved out to easy chairs set in the palace's manicured lawns to begin the discussions, which were to be continued over a dinner.

An Israeli source close to Begin said that among the particular Camp David discussions tonight, Begin also hoped to discuss more general subjects, specifically regional issues such as the recent U.S. downing of two Libyan jets, and the new anti-Western alliance announced last week by Libya, Ethiopia and South Yemen.

After bringing the traditionally upbeat U.S.-Israeli relations to an all-time low by his bombing of Iraq's nuclear reactor outside of Baghdad and his later bombing of civilian residential districts in the Lebanese capital of Beirut this summer, Begin is reportedly hoping his meeting with Sadat will refurbish his image as a man who is really seeking peace.

To that end, Begin has let it be known that he was coming to the talks with several specific proposals to revive the autonomy talks. These are believed to include promises of relaxing the stiff measures Israeli troops have imposed on the Arabs of the occupied West Bank and Gaza territories in the past year and possibly the proposal of a new council of West Bank leaders, made up not only by the pro-PLO urban Arab leadership but of new, and less militant, village chiefs now being courted by Defense Minister Ariel Sharon, who presides as virtual czar over the occupied territories.

There are general doubts among conference sources that these concessions will be enough to appease Sadat and lead him to agree to a reopening of the autonomy talks. Sadat's Foreign Minister, Kamal Hassan Ali, in a carefully timed interview with an Egyptian magazine over the weekend, reiterated the Egyptian view that a resumption of the autonomy talks is not feasible before the U.S. government formulates its own policy. That, Hassan Ali said, could not expected until President Reagan meets Begin, Jordan's King Hussein later in the fall, and Saudi Arabian Crown Prince Fahd sometime in November.