The attack, which came Easter morning as thousands of Christian visitors were worshiping in the Old City, set off furious demonstrations by Arabs throughout East Jerusalem.

Stone-throwing youths injured at least 27 Israelis and foreigners on the Mount of Olives, and two of the injured were hospitalized. On the Temple Mount, hundreds of angry men and boys chanted Palestinian nationalist slogans and stoned a small contingent of Israeli policemen who were quickly reinforced by troops in combat gear who sprayed tear gas and fired into the air.

(Hospital officials said 25 people were treated for gunshot wounds and about 150 were treated for other injuries in the attack and the subsequent clashes, according to United Press International.)

Islamic leaders in Jerusalem declared a one-week general strike, which appeared to hold the potential for further clashes both in Jerusalem and the occupied West Bank, where scattered demonstrations were reported after the incident.

A 17-year-old boy was shot and wounded in Ramallah, north of Jerusalem, by an Israeli soldier whose vehicle was stoned, the Israel radio reported. Mayor Regrets the Shooting

Jerusalem's Mayor, Teddy Kollek, called the shooting at the Dome of the Rock ''a terrible incident, all the more so because of the place where it happened.

''We have all these years guarded the holy places with the utmost care,'' he said. ''We never had anything of this kind happen in 15 years. But mad things do happen.''

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The Temple Mount, an ancient man-made plateau just inside the Old City walls, has repeatedly been a target of agitation by Jewish militants trying to pray there in defiance of a ban by the Israeli authorities. Fistfights have broken out between Jews and Arabs, and arrests have been made.

The mount was the site of the original Jewish temple built by Solomon and of the Second Temple, which was destroyed by the Romans in A.D. 70. There has been no Jewish presence on the mount since then, although it is one of the holiest places in Judaism. Israel, after capturing that part of Jerusalem in the 1967 war, pledged to leave all holy sites undisturbed and in the custody of their religions. Important to 2 Religions

Consequently, the mount and its two mosques - Al Aksa Mosque and the Dome of the Rock, also called the Mosque of Omar - have remained under the jurisdiction of an Islamic council. The site is usually considered the third holiest in Islam, after Mecca and Medina, because a protrusion of bedrock, around which the Dome of the Rock was built in the seventh century, is believed to be the point from which the Prophet Mohammed ascended to heaven on his horse.

The rock is also sacred in Jewish tradition, which knows it as Even Ha-Shetiya, or the stone from which the world was created. Israel's chief rabbis issued a strong denunciation of the gunman today, according to the Israeli radio, declaring that he had desecrated a spot holy to the Jewish people.

According to witnesses, Mr. Goodman entered the Temple Mount through the Gate of the Mughrebins at about 9:30 A.M. He was in a soldier's uniform and was carrying an American-made M-16 rifle, standard issue in the Israeli Army. An army spokesman said he was a soldier but it was unclear whether he was a reservist or a regular.

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In uniform, he had no trouble carrying his weapon through the two checkpoints leading to the mount, where even handbags are usually searched for arms. He approached the ornate, octagonal dome of the rock, which is capped by a golden dome and covered on its facade with intricate marble and mosaic. Old Guard Is Shot

Just to the left of the mosque's western door, a 65-year-old unarmed guard, Haj Saleh Yaman, sat on a white bench. The gunman took aim and shot him dead, witnesses said.

He fired at the mosque, chipping the marble and the mosaic and putting bullet holes in the great brass-plated doors. He shot at people in the vicinity, apparently indiscriminately, wounding two Arab policemen, one of them seriously. Then he entered the mosque.

There were few people inside, according to Arabs who were there. The gunman fired wildly. An Arab about 20 years old was killed, either inside or outside. The number wounded was in dispute, with the police reporting 9 and the Israel radio, which apparently accepted Arabs' figures, saying as many as 40. Reporters who arrived at the scene moments after the incident and saw the injured being taken away said they thought 40 was an exaggeration.

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When the shots rang out, there were large crowds of Jewish worshipers adjacent to the Temple Mount at the Wailing Wall. Several bar mitzvahs were in progress. Suddenly police jeeps and ambulances raced into the plaza near the wall, and the worshipers were herded out, according to Robert Geffen, who was there.

''Everyone just walked very quietly up the stairs leading up to the Jewish quarter,'' he said. The plaza by the wall then became a staging area for troops throughout the morning.

As policemen and riot troops ran onto the Temple Mount, crowds of Arab men ran up as well through other gates and waved sticks and shook their fists, trying to get to the mosque. Policemen surrounded the mosque. There was gunfire. They stormed the building, captured the gunman and ran with him from a side door. The screaming mob chased them as soldiers fired over their heads. Bomblike Object Found

On Friday, an object made of electric wires to look like a bomb was found and dismantled at the entrance of Al Aksa Mosque, Arabs said. Attached was a threatening letter bearing Rabbi Kahane's name, among others, saying, ''We hope that you allow us to pray'' and ''Wait for more operations against you and against Christians, if you continue to oppose us.''

After the mosque was cleared today, the demonstrators turned on the policemen and soldiers. For the next two hours, several hundred Arab youths, chanting ''Palestine is Arab!'' ''Jews out!'' and ''God is great!'' and hoisting a Palestinian flag, demonstrated in the plaza beside the Dome of the Rock.

Eventually the troops withdrew but returned when a small police contingent was stoned. They shot into the air and used tear gas, driving the demonstrators toward Al Aksa Mosque. Most of them left the mount and the soldiers were ordered to withdraw.

Just before going, one of them, with a laugh, threw a tear gas grenade near the mosque, upwind of the main door. Smoke from the perfectly placed cannister blew into the mosque, and worshipers came out coughing and wiping their eyes. One elderly man was carried to an ambulance. A few of the troops walked away laughing. Begin's Statement

Mayor Kollek worried openly about the gunman's attack being taken as an attack by the Jewish people. The Arabs on the mount, many of them in a frenzy of anger, were largely convinced that the assault was part of an Israeli Government plot to expel them from their mosques.

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Prime Minister Menachem Begin issued a statement calling the assailant ''a mentally ill man.'' The statement continued, ''Every man of good will feels deeply the pain in his heart at the terrible sacrilege and loss of life.''

He condemned the Supreme Moslem Council, which called the general strike, and said it was ''attempting to exploit the tragedy.''

---- U.S. Denounces Shootings

WASHINGTON, April 11 (UPI) -The State Department today denounced the shootings in Jerusalem as ''an outrage'' and called the man taken into custody ''deranged.''