Shrill voices of defiance, muted criticism and occasional praise mingled throughout the Arab world today as nations and individuals tried to come to grips with Anwar Sadat's break with a quarter century of Arab hostility toward Israel.

From Algiers to Baghdad, angry Arabs, including some Egyptians, marched on Egyptian embassies, burned Egyptian flags, and denounced the Egyptian president as a traitor to the Arab cause.

Syria declared a day of national mourning to mark what Damascus Radio called a "black day in the history of the Arab nation." At least one person was reported killed in Beirut when some of the estimated 5,000 participants in a protest march tried to storm the Egyptian embassy and gunfire erupted.

Egypt itself was calm. Political and religious organizations and, most importantly, the armed forces, proclaimed their support for Sadat. The president's arrival at Ben Gurion Airport and at the King David Hotel in Jerusalem were carried live on Egyptian television. Crowds gathered around the windows of appliance stores to witness this event that most Egyptians never dreamed was possible. Life otherwise was close to normal.

Sadat's visit coincided with the annual Moslem Festival of the Sacrifice, which falls at the end of the month of the pilgrimage to Mecca and shuts down much of the Arab world for four days. Schools, universities and factories, the most likely sources of organized protest against the government here, are all closed.

This morning, Egyptian television carried live coverage of the hundreds of thousands of Moslem pilgrims at their prayers in the holy city of Mecca, Saudi Arabia. But the departure from Egypt tonight of a different kind of pilgrim, President Sadat, was not shown and was not announced to the public until after he was airborne.

About 500 black-uniformed policemen were on guard at the parking lot of the Ismailia soccer stadium, which Sadat used as an improvised helicopter pad. But their presence seemed to be more for ceremony than security as they far outnumbered the Egyptians who came to see Sadat off.

Two local musical groups performed and some carefully selected young men shouted such slogans as "We Go With You, Sadat" and "Sadat, Champion of Peace."

Sadat, who dislikes his official residence in Cairo and spends most of his time at his other houses around the country, drove up in a black Mercedes limousine, shook hands with a delegation of local notables - including a token peasant - and was gone. His helicopter took him to a nearby military airfield for the hour flight to Israel.

Egyptian political analysts and government officials have sought to dismiss the opposition to Sadat's trip as predictable and transitory. It is too soon to say whether they underestimated the intensity of the reaction but there was strong anti-Sadat feeling in many parts of the Arab world today.

Sadat reportedly is planning to send Vice President Hosni Mobarak on a tour of Arab capitals after his own return from Israel, to explain Sadat's motives to other leaders and brief them on the results of the trip. The Egyptians clearly expect that Israel will give Sadat some substantial gain, perhaps in the form of a gesture to the Palestine Liberation Organization, to bring back with him.

Sadat's visit, a remarkable gesture to a country with which Egypt is still technically at war drew two kinds of opposition. In some countries, such as Tunisia, students and workers tried to attack Egyptian embassies but were held back or driven off by police and troops. Gunfire was reported in Tunis and in Algeria. This kind of action is unlikely to have much effect on Sadat's policy or on the course of events.

But is Libya, which apparently is on the brink of a complete rupture with Egypt only a few weeks after they had restored normal relations in the aftermath of their border war last summer. Although no match for Egypt politically or militarily, Libya can be a nuisance through border incidents, retaliatory moves against the 100,000 Egyptian workers in Libya, and terrorist acts inside Egypt.

A major fire was reported at the Egyptian embassy in Tripoli today and the Libyan news agency said 100,000 took part in protest demonstrations. Hassan Sadiq, the Libyan charge d'affaires in Cyprus, called a press conference to say that Libya would soon adopt a new flag, since its present one is almost identical to that of Egypt, and that Libya would demand Egypt's ouster from the Arab League. The old flags were burned at Libyan legations throughout the world.

Potentially more serious is a surprise statement of criticism from Saudi Arabia, a major financial backer of Egypt and wielder of enormous political and moral force in the Arab world.

Hitherto a supporter of Sadat's peace initiative, Saudi Arabia had been widely reported by the Egyptians and by diplomatic observers to have given at least tacit approval to Sadat's move. Sadat was in Saudi Arabia for talks with King Khaled just before he first proposed this trip early this month.

But a statement broadcast last night on Riyadh Radio indicated that the Saudis are less than enthusiastic about Sadat's decision to strike out on his own with this spectacular gamble.

The statement criticized "hehavior, the consequence of which is not certain," and said the Arab cause was now in a "precarious state."

The Saudis reminded Egypt that they are committed to the principles of the 1974 Arab summit conference at Rabat: the recognition of Palestinian national rights and the withdrawal of Israel from all territories occupied in the 1967 war, "including Jerusalem."

The situation in Beirut is complicated. There, troops of the Arab peacekeeping force that ended the civil war last year were called out to hold off demonstrators at the Egyptian embassy.

That force is dominated by Syria, which is itself strongly opposed to the Sadat trip. Reports of the reappearance of armed men on the streets of Moslem West Beirut, warning merchants to observe the call for a protest strike, stirred unpleasant memories of the war.

Some observers feared that if the Syrians allow a resurgence of violence in West Beirut, which is dominated by Palestinians and Lebanese Moslems, it could touch off a reaction from the Lebanese Christian forces - who have formed an odd alliance with the Israelis.

Criticism of Egypt in other parts of the Arab world, though often vehement, is less likely to be of any real concern to the Egyptians.

Demonstrations were reported in Iraq and Algeria and both governments have denounced the trip, but both have long been out of sympathy with Egyptian policies anyway. The same is true of South Yemen, a Marxist state, which also put out a critical statement.

The United Arab Emirates, also a financial contributor to Egypt, put out a statement regretting "contradictions" in the Arab position, but reminding other states that Egypt has made sacrifices for the Arab cause and for the cause of the Palestinians.