President Hosni Mubarak, concerned about domestic outrage ignited by the U.S. interception of an Egyptian airplane carrying Palestinian terrorists, today demanded a public apology from President Reagan "for all Egyptians."

Mubarak said he had not bothered to read a private letter from Reagan delivered to him yesterday.

"Until now I didn't read this message. Frankly, I am very upset," said the Egyptian head of state.

"I did not receive any convenient apology. This is needed for all Egyptians. All Egyptians should know that. There shouldn't be a personal apology in this matter," Mubarak told reporters after he met with the leadership of the ruling National Democratic Party.

U.S. officials here had described the Reagan letter as a "very good first step" toward smoothing over what Mubarak's government has seen as a humiliation at the hands of its closest ally, the United States.

The Americans suggested that it indicated "a level of understanding" of Egypt's feelings and motivations in the crisis surrounding the hijacking of an Italian cruise ship last week.

U.S. Ambassador Nicholas Veliotes announced yesterday that Washington "deeply regrets" what it saw as the "necessary" diversion of the plane carrying the hijackers when Egypt attempted to release them into the hands of Palestine Liberation Organization Chairman Yasser Arafat for trial.

But the continuing bitterness expressed by Mubarak reflects a deep sense of betrayal felt by many Egyptians who have seen their efforts for peace in the region reduced to chaos by the events of the past two weeks.

Egypt's strong ties to the United States, the value of its peace with Israel, and its confidence in Arafat as a partner in broadening the peace process all have been called into question by the string of crises that erupted with Israel's Oct. 1 raid on PLO headquarters in Tunisia.

These acts of violence, which Mubarak predicted will grow worse because of the U.S. action, "represent serious obstacles" in the peace process, Mubarak told his party.

Ibrahim Naafa, editor in chief of the influential, progovernment newspaper Al Ahram and a close associate of the president, said in an interview that he thinks Mubarak will say, "To hell with the United States, to hell with Israel, hell with the Arabs and hell with the Palestinians" in order to concentrate on his internal problems.

Having gotten deeply involved with all of them, Mubarak "ended up humiliated in front of his own people," Naafa said.

Domestic discontent has been growing since before Mubarak assumed office in October 1981. Although fueled by the rising fervor of Islamic fundamentalism and the continuing debility of Egypt's economy, public anger had been kept far below the flash point.

What the Egyptian government is now attempting to do with its sharp rhetoric toward Washington, according to some of its senior figures, is to create a kind of firebreak to prevent the current foreign policy humiliations from inflaming the opposition.

Since 1976, aid from Washington and the resources freed by peace with Israel have been central to the government's strategy for giving its people some measure of prosperity.

Western diplomats here are quick to point out that Egypt essentially has no choice but to remain friendly with Washington, which now provides more than $2 billion a year in assistance, and the price of this aid continues to be peace with Israel.

But it is precisely this lack of alternatives available to the Mubarak government at the moment that exacerbates its hurt feelings and increases its vulnerability to attack from the opposition.

In violent clashes between police and students Saturday, leftist-led demonstrators repeatedly chanted denunciations of Mubarak as a servant of the United States. Since those riots, Egyptian officials have become increasingly critical of the United States' behavior during and after the hijacking of the cruise ship Achille Lauro.

They note in particular that by diverting an Egyptian plane to capture the Palestinian terrorists aboard, Washington did to a friend -- Egypt -- what it was never willing or able to do to an adversary in the region.

"Now," Naafa suggested, "the other Arabs would say, 'Why should we trust the United States?' If they want to hit back against terrorists , the first they hit are their friends. They don't hit back Libya or Syria. They hit, for their first time, their friends."

Naafa, among others, noted that Egypt just as easily could have refused to intervene Wednesday in the negotiations for the Achille Lauro, as Syria did the day before.

The United States refused to participate in the negotiations, according to both Egyptians and U.S. officials. Yet Egypt was able to end the crisis with the loss of only one person among the 12 Americans and more than 400 other persons aboard.

In order to accomplish this, the Egyptians had called on the PLO for help, and the tactic worked.

But to get the PLO's cooperation in ending the ordeal Mubarak "had to pay something, and what he pays is to tell Arafat we will send the people back to him," one well-informed Egyptian official said.

When it was discovered that an aged American Jewish invalid on board had been killed by the hijackers, Arafat said he would try them.

Mubarak reiterated his belief today that by handing the hijackers over to the PLO he would have tested Arafat's recently avowed commitment to a peaceful settlement of the region's conflicts.

At the same time, however, some Egyptian officials wondered how forthcoming the PLO was with them about its relationship with the hijackers and its intentions to prosecute them.

According to western diplomats, some Egyptian officials tried to contact Arafat when the flight to Tunis with the hijackers was refused landing rights, and discovered that he was nowhere to be found.