Also Friday, one person was killed by police in the West Bank, and several other people were injured in attacks in northern and southern Israel.
It is the latest bloodshed in a wave of violence between Israelis and Palestinians stemming from recent restrictions by the Israeli government on the site Jews call the Temple Mount and Muslims the Noble Sanctuary.
Israeli Prime Minister Benjamin Netanyahu on Thursday urged Arab and Israeli leaders to stay away from one of the country's holiest sites in an effort to keep tensions from getting out of hand.
In a televised speech, Netanyahu asked Jewish and Arab political leaders to steer clear of the area for fear that any visits could spark an "explosive" event. Anger has been brewing among Palestinians over Israeli restrictions on access to the site.
The site is sacred to both Judaism and Islam and, as such, has become a focal point of discord.
In other remarks, Netanyahu was more stern and contentious.
He blamed recent bloodshed on the Palestinian Authority, which has authority in parts of the West Bank, and Hamas, which has authority in Gaza, for what he called their "incitement and libels and lies." He castigated those who used Molotov cocktails, knives and rocks as well as live ammunition against Israeli citizens and security forces.
"All of us, we're in the midst of a wave of terrorism ... terrorists that are incited, filled with hatred and trying to hurt people."
Palestinian Authority President Mahmoud Abbas
said earlier this week that he doesn't want the situation to escalate.
Multiple deaths in Gaza clashes
Islamic Jihad and Hamas called for protests on Friday, in what they called a "day of rage" that began with violent protests in the West Bank, in which Israeli riot police fired rubber-coated steel bullets in an attempt to disperse the crowd.
After prayers Friday, a group of protesters moved east toward a border fence in northern Gaza.
The Israel Defense Forces said in a news release that "more than a thousand rioters infiltrated the buffer zone" and "hurled a grenade, rocks and rolled burning tires" at IDF soldiers. "The forces on site responded with fire on the main instigators in order to prevent their advance and to disperse the riot," the IDF said.
"The riot took place under the watchful eyes of Hamas gunmen, and following [Hamas leader] Ismail Haniya's call today to Palestinians to take up arms," the IDF news release said.
Medical sources in Gaza said that at least three Palestinians were killed at that location -- including a 14-year-old identified as Shadi Dalalah -- and at least three others were killed during clashes in Khan Younis in southern Gaza.
Thirteen Palestinians have been killed in violence in the past week, the Palestinian health ministry said.
Referring to the incident in northern Gaza, Riyad Mansour, Palestinian ambassador to the United Nations, said in a letter Friday to the president of the U.N. Security Council that the IDF forces "fired at peaceful demonstrators in an area east of Al-Shujaiyeh neighborhood," and identified four people who were killed.
Mansour denounced "Israel's intensification of its onslaught against the Palestinian people."
"Words are not enough and action must be taken to compel Israel, the occupying Power, to halt its illegal and destructive policies and practices," Mansour wrote, adding that the Palestinian people "cannot remain the exception to the responsibility to protect civilians from such atrocities and flagrant breaches of the law."
Multiple injuries at multiple locations
Incidents of violence Friday were reported at multiple locations in addition to the clashes in Gaza.
-- A Palestinian woman was shot to death near Hebron in the West Bank after attacking a police officer at the Kiryat Arba settlement, Israeli police said.
Israeli police spokeswoman Luba Samri said a "terrorist" attempted to take the officer's weapon and stab him, and that police nearby shot and killed the assailant. The police officer was lightly wounded, Samri said.
-- In the Israeli city of Dimona, in the Negev desert, south of the West Bank, two Bedouins and two Palestinians were wounded in attacks by a knife-wielding man near a school Friday morning, Samri said.
A 20-year-old Jewish resident believed to have carried out the attack is in custody, Israeli police spokesman Micky Rosenfield said. He said the suspect told police he carried out the attacks because "all Arabs are terrorists."
-- A 16-year-old Jewish boy in Jerusalem told police that "an Arab" punched him and then ran away, and the boy gave chase before realizing he had been stabbed. He was lightly wounded in the upper part of his body and is receiving medical attention, Samri said.
Police said they have arrested an 18-year-old Palestinian who fit the description of the assailant and continue to search for the weapon.
-- Border police officers shot and wounded an Israeli Arab woman after she tried to stab a soldier waiting for a bus in Afula in northern Israel. Originally authorities identified the woman as a terrorist. On October 29 they said she was trying to induce police officers to kill her. She was charged with holding a knife and making threats.
Three Israelis stabbed Thursday
In Tel Aviv, a female Israeli soldier was stabbed with a screwdriver, allegedly by a Palestinian, on Thursday. Another soldier shot the attacker dead, said Samri, the Israeli police spokeswoman. The attack left four people lightly wounded, including the soldier.
In the Kiryat Arba settlement in the West Bank city of Hebron, an Israeli man was in serious condition after being stabbed in the stomach, Samri said. Israeli security forces are still looking for that attacker.
--Also Thursday, a Palestinian stabbed an ultra-Orthodox Jewish student, 25, in Jerusalem, wounding him seriously, police said. A 19-year-old Palestinian from the Shuafat refugee camp has been arrested in that attack at a light rail station near Jerusalem's main police headquarters.
Holy site at heart of dispute
Muslim men under age 45 will be prevented from attending prayers at what they call the Noble Sanctuary. Another security assessment will be made before Friday prayers, Israeli police said.
Palestinian protesters have repeatedly clashed with Israeli security forces in and around the complex in recent weeks.
The move by Israeli authorities to prevent Muslim men under 50 from attending prayers at the site angered Palestinian leaders. It followed an attack Saturday in which two Israelis were killed.