Egyptian President Anwar Sadat and Israeli Prime Minister Menachme Begin apparently failed to reach agreement on a single substantive Palestinian issue in the Middle East peace negotiations that ended here today after three intensive meetings, despite the pressure to reach agreement on self-rule in the territories occupied by Israel.

That conclusion emerged from statements by both leaders at the end of their talks, and from informal assessments by their top advisers after Begin left Lower Egypt at the end of what appears to have been little more than an elaborate government-conducted antiquities tour for the benefit of Begin and his entourage.

Begin roamed the upper Nile in Sadat's handsomely appointed presidential jetliner -- visiting such monumental ancient Egyptian sites as the temples of Karnak, the tombs of the Valley of the Kings and the splendor of Abu Simbel near the Sudanese border -- but he came away with something that seemed of less lasting importance.

Sadat resuscitated a plan he advanced more than a year ago by proposing that Israel's idea of limited self-rule for the 1.1 million Palestinian Arabs in the West Bank and Gaza Strip be implemented first in the Gaza Strip, which between 1948 and the Israeli-Arab six-day war of 1967 was occupied by Egypt.

Seizing upon the suggestion, Begin said he would present a "Gaza first" proposal to his Cabinet as early as Sunday. But Sadat immediately countered with the caveat that autonomy for the approximately 500,000 Gazans could not be put into effect until agreement was reached on the future self-governance of all Palestinians in the occupied territories.

That condition appeared to cast doubt on the prospect of using the Gaza Strip as a model for later autonomy application in the West Bank, where opposition to any self-rule plan not approved by the Palestine Liberation Organization is most intense.

It reinforced doubts expressed last month by President Carter's Middle East envoy Sol Linowitz that the goal of establishing an autonomous Palestinian administration in the occupied West Bank by this May can be met.

Ironically, the negotiations on implementing autonomy in the narrow strip came just as Moslem fundamentalists rampaged briefly in the streets against secular influences, burning several stores and cafes where liquor is sold and ransacking a movie theater.

Although the disturbances ostensibly are linked to a leftist-conservative power struggle over the control of a small university, Palestinian sources described the violence as an outgrowth of mounting opposition to the normalization of relations between Egypt and Israel.

While Sadat pressed Begin during the summit for a softening of Israel's stand on the toughest of the issues surrounding the autonomy plan -- the status of East Jerusalem in the electoral process leading to Palestinian self-governance and the limits of power of the proposed self-governing council -- there were no agreements on those issues, according to both leaders.

In a meeting with reporters at the end of the summit, Begin made it clear that he had tried to steer the discussions toward speeding up the process of normalizing relations between the two countries after the Israeli Army withdraws on Jan. 26 from approximately half the Sinai Peninsula, roughly behind a line stretching from El Arish in the north to Ras Mushammed in the south. a

Begin said that "attempts were made to weaken this process," but he said the one issue he insisted on pressing to a conclusion was direct air flights between Tel Aviv and Cairo. As a result Begin said, Egyptair, Egypt's national airline, and El Al, Israel's counterpart, will begin direct routes after Jan. 26.

Begin said Sadat had promised direct air routes during their meeting last summer in El Arish. While the Israeli prime minister suggested Egyptair was ready to begin flights, Egyptian officials indicated that such a link might create some problems for the airline with Persian Gulf states. Observers said El Al might inaugurate the route in both directions, splitting revenues with Egypt on return flights.

Begin and Sadat made it clear in statements to reporters that they did not even come close to an understanding on the future of Jerusalem, which Begin called "eternal and indivisible."

But the two leaders said they are in accord on the formidible strategic questions facing the Middle East and eastern Asia in the wake of the Iranian upheaval and the Soviet invasion of Afghanistan, even though mutual military cooperation is unlikely at this time.

They both condemned the Soviet invasion, and Sadat noted that he had already pledged military cooperation with the United States in the defense of any Arab state.

In a television interview broadcast by the Israeli television tonight, Sadat said strategic cooperation would have to be secondary to the Palestinian issue for the time being.

"Out main concern now should be for the momentum of the comprehensive peace process," Sadat said. "The geopolitical situation enhances the need to complete the peace process. . . . "