Only Israeli citizens, Old City residents, tourists, businesspeople working in the area and students studying there will be allowed to enter, police said in a statement Sunday.
They said they're also preventing Muslim men under the age of 50 from attending prayers at the holy site in the Old City that Jews call the Temple Mount and Muslims call Haram al-Sharif, or the Noble Sanctuary.
Palestinian officials reacted angrily to the move.
"What's happening today is a renewal of Israeli arrogance and recklessness," Hatem Abdul Qader, a Jerusalem official for the governing Palestinian party Fatah, told Palestine TV. "Jerusalem is now a military base, sons of Jerusalem are now banned from entering the Old City."
The measures follow the knife and gun attack Saturday by a 19-year-old Palestinian in the Old City in which two Israelis were killed and two others were wounded, according to authorities.
Police say they killed the attacker in a gun battle. He was identified as Mohannad Shafik Halabi from near Ramallah, in the West Bank.
Early Sunday, a 15-year-old Jewish boy was wounded in a stabbing attack by an Arab in a Jerusalem neighborhood near the Old City, Israeli police said. Police shot and killed the attacker, a spokesman said.
The official Palestinian news agency WAFA disputed the Israeli account of the incident, reporting that a 19-year-old Palestinian man was chased by Israeli settlers and then shot by police.
Tensions on the rise
The bloodshed over the weekend is the latest in a spiral of violence and escalating tensions in the region.
Palestinian protesters have repeatedly clashed with Israeli police at the Temple Mount in recent weeks. The turmoil has spread to other areas as well.
Last week, an Israeli couple were shot and killed
in the West Bank in front of their four children, according to Israeli officials.
And anger boiled the week before among Palestinians over the death of a teenager
who was shot by Israeli soldiers at a military checkpoint at Hebron in the West Bank. The Israeli military said she attacked a soldier with a knife, an account disputed by Palestinian sources.
The United Nations issued a statement on behalf of Secretary-General Ban Ki-moon Sunday
condemning "in the strongest terms" the attacks in the Old City of Jerusalem and subsequent incidents.
"Recalling the recent deadly attack on another Israeli family in the occupied West Bank, and in light of the wave of extremism and violence sweeping the region, the Secretary-General is deeply concerned that these latest incidents signal a dangerous slide towards escalation," the statement said. "The Secretary-General is deeply troubled by statements from Palestinian militant groups, including Hamas, praising such heinous attacks."
The U.S. State Department issued a statement Saturday
, saying it "strongly condemns all acts of violence, including the tragic stabbing in the Old City of Jerusalem today."
"We are very concerned about mounting tensions in the West Bank and Jerusalem, including the Haram al Sharif/Temple Mount, and call on all sides to take affirmative steps to restore calm and avoid escalating the situation," the statement said.