Secretary of state Cyrus Vance and Egyptian President Anwar Sadat opened talks last night that may determine the fate of the Middle East peace initiative launched by Sadat with his visit to Jerusalem eight months ago.

U.S. and Egyptian officials agreed that the outcome of these talks will be crucial in determining whether the peace initiative will go on. But neither side indicated in public that it had new proposals to break the deadlock in direct Egyptian-Israeli talks, which were suspended by Sadat July 30.

Vance and Sadat met for two hours last night, but spokesmen gave no indication of how the talks had gone. The two are scheduled to meet again tonight. Vance will return to Washington tomorrow to report to President Carter.

Vance arrived in this Mediterranean port and beach resort in the early afternoon after a 40-hour visit to Israel that was hailed by prime minister Menachem Begin as the best meeting the Israelis and Vance have ever had. The Israelis said Vance had not asked for new concessions to get Sadat back to the peace table.

The perception by Israeli officials that the pressure they have felt during much of the Carter administration has eased for the moment was balanced here by Egyptian doubts about American support for Sadat's peace efforts. The Egyptians were stung by a public rebuke from the State Department, which called Sadat's move to suspend talks with Israel "deeply disappointing," and they are puzzled by American failure to bring forward a plan to get the two sides talking again.

The Egyptians believe they have made substantial concessions that have not been matched by Israel. They note that Sadat has dropped the Arab demand for an independent Palestinian state and has omitted any mention of the Palestine Liberation Organization from his proposals for a settlement of the most difficult issue, the future of the West Bank of the Jordan River.

A new Israeli proposal on the West Bank apparently is what triggered Sadat's declaration July 30 that Egypt would not engage in further direct talks until Israel agreed in principle to a total withdrawal from all the Arab territories it occupied in the 1967 war.

The Israelis said at a meeting of U.S., Israeli and Egyptian foreign ministers in England last month that they would discuss some form of "territorial compromise" on the West Bank after a five-year period of local self-rule and continued Israeli military occupation.

The state department saw this as an expression of new flexibility on the part of the Begin government, which previously had refused to consider giving up any of the West Bank. Sadat, however, regarded it as a maneuver to make him agree that part of the West Bank would go to Israel, and he reacted sharply.

New doubts about the strong U.S.-Egyptian ties that have developed since the 1973 Arab-Israeli war surfaced yesterday in an editorial in the Cairo newspaper Al Ahram, which often reflects official thinking on foreign policy. The editorial noted caustically that "no progress has been made" since President Carter met Sadat at Aswan and agreed publicly that a negotiated peace must be based on Israeli withdrawal from "all fronts" and on a "solution to the Palestinian problem in all its aspects."

After criticizing the present U.S. stand as "ambigious," the newspaper observed, "The question now is does the U.S. administration really have any new suggestions? The Middle East crisis cannot be allowed to drag on like the disarmament problem or the North-South Korean talks for a quarter of a century."

Vance and Foreign Minister Mohammed Ibrahim Kamel emerged from two hours of exploratory talks yesterday afternoon with nothing to report to waiting journalists. Asked whether the talks had been satisfactory, Kamel said only that they were continuing.

Vance did not talk to reporters on the Air Force jetliner that took him from Ben Gurion Airport to the Egyptian military air base at Gianaclis. He was ferried about 50 miles by helicopter from there to Alexandria, but did not meet Sadat until 9 p.m., after the Egyptian leader had finished the traditional meal that ends the day of fasting for Moslems during the month of Ramadan.