The most violent clashes between students and police here since the turbulent final years of Anwar Sadat's rule erupted outside Cairo University today. The rock-throwing melee apparently prompted a public denunciation by President Hosni Mubarak of the U.S. seizure of an Egyptian plane, coupled with a plea for calm to his countrymen.

The riot by hundreds of students and other Egyptians, coming in the wake of the interception of the airliner carrying the Palestinian hijackers of the Italian cruise ship Achille Lauro, appeared to have deeply shaken Mubarak, whose government already has been dealt heavy blows by events in the region during the past two weeks.

In impromptu remarks to reporters late this afternoon, Mubarak's tone was bitter as he made his first public comments on the U.S. action.

He said he was "wounded" by what he termed the United States' act of "piracy" in intercepting the airplane with F14 fighters late Thursday night and forcing it to land in Sicily early Friday morning.

Mubarak said that before the fighters were identified, "I would never have imagined it to be a friendly country."

"I was shocked when I heard it was the United States. We had not expected this attack from a friend," Mubarak told the journalists after meeting with Sudan's prime minister.

Mubarak has been embarrassed further by charges that he lied Thursday when he said at about noon that the hijackers had left the country before he knew that they had killed an American.

Today he admitted that the terrorists actually had left at about 10:15 p.m. Thursday, but he asserted that for "technical, administrative and political reasons, I did not know the hijackers had not left until three hours after my announcement."

A report in the semiofficial Al Ahram newspaper today suggested that although the president had given the order early in the day to let the hijackers leave accompanied by PLO and Egyptian officials, there were delays in chartering a plane and getting permission to land in Tunisia.

The same report, regarded as an authoritative Egyptian statement by western diplomats here, said the United States learned from Egyptian-Tunisian communications about the plane the information necessary to intercept it. The report implied that the United States monitored these communications and may have encouraged the Tunisians to stall until the plane was in the air, then asked them to revoke the landing rights when the plane was vulnerable to interception.

Mubarak appeared unswayed this afternoon by President Reagan's suggestion yesterday that "there is too much at stake with regard to peace in the Middle East for us to let a single incident of one kind color that relationship."

"Now there is a coolness and strain as a result of this incident," Mubarak said. "Go down and ask the people how wounded they feel. Some of the people are already expressing these feelings."

"I am asking Egyptians and university students to be wise and be calm," Mubarak said.

But among the students and other Egyptians it was clear today that the U.S. interception of the plane was only the latest in a series of incidents that have served to humiliate Mubarak and have left his foreign policy in disarray.

The demonstration was called last week after Israeli jets staged a devastating raid on the headquarters of the Palestine Liberation Organization in Tunis. Other rallies held here during the past several days to denounce that raid have been peaceful.

But today, before the violence began, the anger against the United States and Israel and against Mubarak, for his cooperation with them, was evident.

"The American people must know the truth about the Egyptian people," an engineering student shouted at a reporter. "They have had enough of Mr. Reagan and American policy toward the Middle East and the people of Palestine."

"Hosni Mubarak, you are the servant of America," the students chanted as they burst through the gates of the university and into the streets shortly before noon.

Instead of marching toward the Israeli Embassy, within sight about five blocks away, about 500 demonstrators swerved toward crowded Giza Square, picking up support along the way from students leaving classes who in the past often remained on the sidelines.

As hundreds of riot police deployed before them, the demonstrators shouted at the troops, "Are you the soldiers of Egypt or of Israel?"

The clashes began as the police charged the students, swinging batons and chasing them for a block before the demonstrators began to respond by throwing rocks and pieces of pavement. The sound of tear-gas guns firing reverberated through the streets.

Later, when the gas was clearing, the students found the canisters, labeled "M518 Riot CS, Federal Laboratories, Salisbury, Pennsylvania," and the anti-American mood grew more intense. Western reporters found themselves increasingly harassed by the crowd, now reduced to a hard core of about 150 demonstrators still confronting the police.

In all, 15 protesters were seen being arrested, and about an equal number were injured. A police colonel on the scene said that none would require surgery.

Since Sadat's assassination in October 1981, Mubarak has tried to broaden political participation in the country slowly and to dispense with the heavy-handed suppression of dissent that marked his predecessor's government in its final years.

Generally, marches have been permitted and have been peaceful. Egyptians, particularly residents of the crowded capital, are known for their patience and good humor.

But Mubarak's economy is deteriorating. His new Cabinet, appointed last month, is seen as auguring more austerity. Furthermore, his delicately calibrated attempts to improve relations with Israel and work with the United States for a broad Middle East peace process while ending Egypt's isolation in the Arab world have come to next to nothing.

The Israeli raid last week and the American interception this week were seen by many Egyptians as proof that Mubarak's foreign policy is fruitless.

The blow was not softened by Italy's role, as Italian Prime Minister Bettino Craxi had been regarded as a key Arab ally.

"He is our friend," Mubarak said. "I am very sad that he should let American fighters intercept an Egyptian civilian plane . . . ."

The fact that senior PLO officials were on board the diverted plane and suggestions, particularly in the American press, that Mubarak somehow may have acquiesced in its interception have weakened his position among Arab states as well.

"Is it so easy to overlook such an incident?" Mubarak asked, referring to the Reagan administration's attempts to sound conciliatory after the plane's diversion. "We are friends, but to be able to overlook this incident, it will take a long time."