President Hosni Mubarak's moment of public fury during an impromptu press conference a week ago has been run and rerun on Egyptian television during the past few days.

Mubarak lashes out at the United States for intercepting an Egyptian jet carrying the four Palestinian hijackers of an Italian cruise ship. "What country would commit an act of piracy like this?" he demands. How could it have been Egypt's friend, the United States? And then the president says what many Egyptians have felt. "I am deeply wounded," he tells the reporters.

Deputy Secretary of State John C. Whitehead, who arrived today in an apparent attempt to smooth things over, was likely to find a man who needs more than kind words to heal the hurt he expressed so openly. Mubarak is to see Whitehead Monday.

The crises of the past three weeks, starting with the Israeli raid on Palestine Liberation Organization headquarters in Tunisia, have forced Mubarak to confront a dependency on American economic assistance that has turned from a source of good will to the root of his humiliation.

Although he is angry at the actions of Israel and those of the United States, he is not known to have found an alternative to U.S. support. Yet his display of emotion seems to have had a tonic effect on this society.

Egypt had been accustomed to the messianic Gamal Abdel Nasser and his successor, the ruthless, sometimes reckless visionary of peace, Anwar Sadat. After four years, it is still getting used to the caution of Mubarak.

Until recently, he was joked about commonly as "the laughing cow," after the brand name of a bland cheese sold in Cairo's markets. He has been described as a shadow of Sadat, as a former fighter pilot used to reading gauges and lacking the ability to see beyond mechanical, technocratic answers to the nation's complex problems.

But with the string of crises this month, Mubarak has faced the hardest tests of his administration. And if he appears to be weakened for the moment, there are also signs that he and his country are wiser about each other.

Cairo University political scientist Ali Dessouki said of the president's televised outburst, "It was not an act. It was not something he played." Mubarak's predecessors might have postured, but his voicing of "anger, anguish, disappointment and letdown" was real, Dessouki said.

"Had he not done that, the public outcry would have been much more violent," Dessouki suggested, in a view now also common among western diplomats. "He almost acted as a safety valve."

In the week since, several mass rallies have been called by the opposition, but most have failed to convene.

Today there was a lengthy confrontation at Ain Shams University as police broke up a banned demonstration and, in the process, appeared to have set fire briefly to two university buildings with their tear-gas canisters. Several arrests and a handful of injuries were reported.

Such demonstrations surprise and shock Egyptians because violence is so rare in this society. But outside of such actions by small, militant groups of students, the streets are calm. The national mood, reflected in the press and in conversations, remains tense and angry, but the country appears in hand.

One senior western diplomat summed up the public reaction with a cliche about the Egyptian people's long-cultivated patience: "Don't think that this is a society that is given to questioning the pharaoh or his pronouncements."

Yet even as Mubarak's subordinates speak with growing assurance about the country's continued stability, their most frequent warning is that the West, especially the United States, cannot take Egypt or its president for granted.

Just as this country grew used to the strong hands of Nasser and Sadat, the world was accustomed to dealing with one man who spoke for Egypt and then forced the country into line behind him.

Mubarak's domestic strategy, on the contrary, is based on a gradual but steady opening up of the country's political franchise. His security forces remain pervasive, but with an election last year and extensive freedom for the printed press, he has lifted the lid on countless voices sharply critical of his policies.

Few people except Mubarak describe Egypt as a democracy, but it is experimenting seriously with democratic institutions.

"He wants to know the pulse of the people before taking a decision," said one of Mubarak's spokesmen, Mamdouh Beltagy. "That's very important for him: the cares of the Egyptian people. How are they thinking?

"The most important lesson he learned from Sadat" -- who was assassinated in October 1981 -- "is that he has to take great care of the Egyptian people," Beltagy said.

On Wednesday, Mubarak held an unprecedented meeting with the leaders of all the major opposition political parties. This was interpreted by some observers as a sign of his shaky position. But by consulting with his opponents, he also made them share some responsibility for keeping order.

As he did earlier this year, with necessary price increases and the challenge of Islamic fundamentalists demanding the imposition of strict religious law, Mubarak has kept his domestic opponents guessing and given them no place to focus their blows.

When force has been necessary with crowds, it has been used firmly and, if not with reserve, at least without live ammunition.

Yet the nation's outraged sense of frustration and helplessness since the Israeli raid in Tunisia and the interception of Egypt's Boeing 737 this month has not gone away.

Mubarak, having shared in this feeling publicly, now has to deal with it.

Both his aides and U.S. diplomats say they expect to look seriously at the terms, if not the substance, of Cairo-Washington relations.

Mubarak's economic strategy is based on more than $2 billion a year in U.S. aid, and the aid is conditioned on peace with Israel. Reductions in the cost of defense have also freed desperately needed funds for development.

Egypt "is 50 million people living on arable land the size of the state of Maryland," as one diplomat summed up the situation. The political heat under the weight of so much densely packed humanity is often talked of in terms of spontaneous combustion.

One functionary at the Israeli Foreign Ministry suggested recently that, for Mubarak, "It's very important that peace be there. Because Egypt is a country that can be ignited."

But less because of Egypt's actions than those of its partners, peace has also become a burden.

Mubarak has hoped throughout his term to bring together his relatively new friends, Washington and Jerusalem, with Egypt's old, Arab ones, who had kept their distance since the Camp David accords.

This approach in this hate-filled region has kept him "constantly caught in the cross fire," as one aide put it.

The Israeli raid on Oct. 1, then the events surrounding the Achille Lauro affair, have left Mubarak seeming very much the nice guy who finishes last on the international front.

"He is in a difficult position -- there is no doubt, a very difficult position," said Ahmad Beha Eddin, considered a moderate intellectual.

This month's events, Beha Eddin said, "demonstrated to the people what many people used to say. While he always talked of the relationship with Washington as one of mutual friendship, the other point of view is no -- once you tie yourself economically to the U.S., whether in arms or bread, you can't be your own master. The biggest embarrassment for him is that it proved what the opposition said is true."

Outside the radical opposition, however, one encounters little serious talk of breaking relations with Israel or making strong diplomatic gestures against the United States.

But the desire is strong to show that Egypt has not been "bought," and that while it wants and needs U.S. assistance, it cannot be expected always to toe Washington's line.

At the same time, there is hope for some dramatic sign in the near future, after so much hurt, of a little help from Egypt's friends.

Mubarak has asked for a public apology for the diversion of the Egyptian plane. President Reagan has said no. But more often, Egyptian officials say they are looking for some new move from Washington to begin reviving the regional peace process. If it comes, Mubarak's apparent impotence could be shown as wise patience.

The Egyptians are looking for some movement on the issue of an international conference as a transitional step toward direct talks between Israel and a Jordanian-Palestinian delegation.

When Mubarak was in Washington a month ago, said a Foreign Ministry official, "there was a glimmer of hope" on this issue. Now, he said, that light has to be found once again, "and the sooner, the better."