Egypt recovered sovereignty over the strategic Mitla and Giddi passes today, completing the first phase of Israel's Sinai withdrawal and clearing the way for the first normal diplomatic relations between Israel and an Arab state.

The turnover of an additional 5,500 square miles of Sinai desert, a process begun earlier this week with Israeli troop withdrawals, left Egypt in control of two-thirds of the peninsula and marked a major milestone in execution of the peace treaty signed by President Anwar Sadat and Prime Minister Menachem Begin last March in Washington.

It set the stage for the beginning of formal diplomatic relations between Cairo and Jerusalem on Saturday, making Egypt the first Arab nation to formally welcome Israel into the Middle East after 32 years of struggle. The opening of official ties will underscore Egypt's exit from the rest of the Arab world, which remains adamantly opposed to the recognition of Israel. t

The Palestine Liberation Organization and its supporters in Beirut called a nationwide general strike in Lebanon on Saturday to dramatize their opposition.

In today's ceremony at El Meliz near the Sinai passes, Egypt's Brig. Gen. Abd-Rab Nabi Hafez raised the Egyptian flag as the Israeli Star of David was lowered to signify the restoration of Egyptian sovereignty for the first time since the 1967 Middle East war.

"The recovery of this part of the Sinai shows clearly that wars are not always the only solution for the restoration of the rights of nations," said Hafez, the Egyptian chief of military operations.

The turnover left Egypt in control of all the Sinai west of a line from El Arish on the Mediterranean to Ras Muhammed at the southern tip of the 25,000-square mile peninsula. Restored in stages since the peace treaty, the territory includes seven airfields, the Sinai's major oil fields and its largest military base at Bir Gafgafa.

The remaining third, back to the 1948 international boundary between Egypt and Israel, is to be turned over in April 1982. In the meantime, the opening of normal diplomatic relations Saturday and a formal exchange of ambassadors one month later is in principle to signal open travel between the two formerly hostile neighbors.

Gen. Kamal Hassan Ali, the Egyptian defense minister, said after talks with his Israeli counterpart this week that pending more complete arrangements only one land route between the countries will be authorized and he cautioned that only travelers with visas will be allowed through, in effect, eliminating most Israeli and Egyptian tourism. The possibility of travel for foreigners, many of whom do not need prior visas, was left unclear.

Also unclear was the timing of direct air flights, agreed on in principle by Sadat and Begin at their summit in Aswan early this month. Since then, Egyptian Foreign Ministry officials have insisted that Israel must make concessions in the Palestinian autonomy talks before the Egyptian bureaucracy will actually allow the flights to begin. In any case, they added, Egypt's national carrier, Egyptair, will not fly soon to Israel, even if the Israeli line El Al is allowed into Cairo.

These steps are part of a concerted campaign in the Foreign Ministry to exact more Israeli concessions in the autonomy talks as the price of further normalization steps such as additional tourism visas, commercial ties and cultural exchanges. One high official was quoted as saying establishment of normal relations will be like a "canal through which no water passes" unless the autonomy talks show some progress.