The death toll for the past two days rose to seven as the Palestine Health Ministry reported another Palestinian was killed during a separate clash outside the city. However, it did not provide details of how he died.
In the West Bank, Israeli forces raided the home of the Palestinian attacker who fatally stabbed the three Israelis and wounded another on Friday.
The attacker, Omar Alabed, who invaded their home, was shot and taken to a hospital for treatment, the military said.
An Israeli military spokeswoman said the attacker's brother was arrested and that security forces were restricting movement of Palestinians from his village.
Three Palestinians were killed hours before the attack in violence spurred on by Israel’s installation of metal detectors at entry points to the Noble Sanctuary-Temple Mount compound in Jerusalem's walled Old City.
Tensions over the site, known to Muslims as Haram al-Sharif and to Jews as the Temple Mount, have increased in the few days.
Russia, the United States, the European Union and the United Nations said in a joint statement they were "deeply concerned by the escalating tensions and violent clashes taking place in and around the Old City of Jerusalem", and called for restraint on all sides.
Diplomats said the UN Security Council would meet to discuss the situation on Monday.
Sweden, Egypt and France requested the meeting to "urgently discuss how calls for de-escalation in Jerusalem can be supported", Sweden's Security Council coordinator, Carl Skau, posted on Twitter.
Israeli police said they used riot gear in Jerusalem to disperse dozens of Palestinians who threw stones and bottles at them. Television footage showed police throwing stun grenades and using a water cannon to break up the crowd.
The Palestinian Health Ministry said two Palestinians died of gunshot wounds in two neighbourhoods of East Jerusalem, some distance away from the epicentre of tension. It later reported a third Palestinian fatality.
Major General Yoav Mordechai called on the Muslim world to put forward other suggestions.
"We hope that Jordan and other Arab nations can suggest another security solution for this (problem)," Mordechai told BBC Arabic.
"Any solution be it electronic, cyber or modern technology: Israel is ready for a solution. We need a security solution; not political or religious."