The unprecedented closure of the Old City to Palestinians comes as Israeli Prime Minister Benjamin Netanyahu promised "an all-out war against Palestinian terrorism."
Sunday brought waves of arrests of Palestinians and violent demonstrations across the West Bank, with local media reporting that more than 70 Palestinians were injured by rubber bullets and live rounds during clashes.
Israeli police said the two-day closure of the Old City was intended to protect visitors arriving to celebrate the Jewish holiday of Sukkot.
"This is a drastic measure that's being taken in order to make sure there are no further attacks during the Jewish festival, where you can see thousands of people visiting the Old City," Israeli police spokesman Micky Rosenfeld said, according to the Associated Press.
Israel and the West Bank have been on edge since the deadly knife attack late Saturday and the fatal shooting of an Israeli couple driving in the West Bank on Thursday.
According to Israeli police, a Palestinian teenager attacked Aharon Benita, 22, an off-duty Israeli soldier, his wife and their young daughter near the Lions' Gate in the Old City on Saturday night. The soldier was wearing civilian clothes. The couple had their 2-year-old son and an infant daughter in strollers
Hearing the cries of Benita's wife, Rabbi Nehemia Lavi, 41, who lives in the Muslim quarter of the Old City, ran to confront the assailant.
Lavi and Benita were fatally stabbed. Benita's wife, Adele, was seriously wounded. The couple's 2-year-old son was lightly injured.
"I yelled 'please help me!' and they just spat at me," Adele Benita said of the surrounding Palestinian shopkeepers in an interview with the Israeli news site Ynet.
Lavi was a married father of seven and a leader of a Jewish religious school run by Ateret Cohanim, an organization dedicated to displacing Palestinians in East Jerusalem and the Old City and creating a Jewish majority there.
Thousands attended Lavi's funeral in Jerusalem on Sunday, including Zev Bareitan, whose daughter has married into the Lavi family. He called Lavi "a hero," and said Lavi's oldest son "told us his father wasn't murdered. His father was killed fighting the enemy. He heard screams and knew it was a terror attack. He died fighting a terrorist."
Bareitan said security in the Old City was "very limited," and he called on the Netanyahu government to crack down.
"We're a country at war," he said.
Israeli President Reuven Rivlin said in his eulogy for Lavi, "We will reach the killers of the innocent and pure, and we will reach their inciters and their dispatchers and will deliver them a stinging blow."
The 19-year-old Palestinian assailant, Mohannad Halabi, was a law student studying at al-Quds University. He was shot dead at the scene by police.
His Facebook page warned that "the third intifada has begun" and suggested that the uprising was a reaction to Israeli provocations at the al-Aqsa mosque site, the raised esplanade in the Old City known to Jews as the Temple Mount and to Muslims as the Noble Sanctuary. It is a place holy to both.
"What's happening to our holy places, what's happening to our mothers and sisters in al-Aqsa mosque? We are not the people who accept humiliation. Our people will revolt," Halabi wrote.
His father, Shafeek, a plumber, said he was proud of his son.
"He was a very smart kid with a strong personality. He wanted to be a lawyer to defend the Palestinian people against Israeli brutality," he said.
Shafeek spoke as his children hung a large banner of the Islamic Jihad, a Palestinian militant group, across the entrance of the family's house in the village of Surda, a few miles north of Ramallah in the West Bank.
The family had already emptied their home of possessions, expecting the Israelis to carry out a demolition order.
"I am so proud of him. He defended the honor of 1.5 billion Muslims all over the world. He will be missed not only by me, but by every free decent human being," the father said.
Israeli security forces and Palestinian youths have fought at the front door of al-Aqsa mosque in recent weeks, and Israeli authorities have restricted access to the mosque by age and gender.
They have also outlawed a Muslim organization that brought men and women to the mosque to stand guard and to harass Jewish visitors who enter the compound escorted by armed Israeli soldiers.
The civilian guardians, known as Mourabitoun, or defenders of Islam, say they are there as volunteers to protect the site from Jewish extremists.
But Israel says the guards have triggered clashes over the past two years .
Israeli police said the Old City would be off-limits for 48 hours to all Palestinians who do not live, work or study there. Israelis and tourists would be welcome.
The walled Old City, less than half a square mile, was captured by Israeli forces during the 1967 war and annexed as part of the Jerusalem municipality. Most of the world considers the Old City occupied territory; Israel disputes this.
On Sunday, the Old City's Muslim Quarter was deserted and its shops shuttered.
Jerusalem Mayor Nir Barkat praised the decision to close the Old City to Jerusalem's 300,000 Palestinian residents.
"It's a good, specific solution. This is a correct example of how the police needs to act," Barkat told the newspaper Haartez. "The closure is intended to protect Jews who only want to pray."
Early Sunday, Israeli police said, another Palestinian teenager stabbed and wounded a 15-year-old Israeli near the Old City's Damascus Gate.
Video footage of the scene shows onlookers pointing at the alleged assailant and calling out, "Shoot him!" The video shows a police car arriving and multiple shots being fired.
Palestinians ask why the teenager was shot dead instead of being arrested.
After condemning violence against innocent civilians, Palestinian leader Hanan Ashrawi said, "Netanyahu is under the delusion that he can convince his own people and the international community that he can 'manage the situation.' This is not only morally deplorable, it is also politically irresponsible and effectively unsustainable. Never has a people under foreign occupation accepted the systematic violation of their rights and freedoms."
Sufian Taha in the West Bank contributed to this report.
