The early-morning demolition targeted the property of Abdel Rahman al-Shaludi, who killed two people last month when he plowed his car into a crowd waiting at the Ammunition Hill station of Jerusalem's Light Rail on October 22. The attack killed a three-month-old baby girl and a 22-year-old woman.
Al-Shaludi, 21, was shot by the police as he fled, later succumbing to his wounds.
Amid a wave of unrest, two Palestinians from the annexed east Jerusalem yesterday carried out one of the most gruesome killings reported in the holy city since 2008 when a Palestinian killed eight people at a religious school.
All the victims of the yesterday's attack were Israelis with dual nationality, three of whom were Americans and a fourth British. The fifth was an Israeli policeman.
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Responding to Tuesday's attack, Netanyahu said: "I have ordered the destruction of the homes of the Palestinians who carried out this massacre and to speed up the demolitions of those who carried out previous attacks."
Netanyahu also held an emergency security meeting he called to discuss ways to stop the wave of deadly attacks.
The IDF said the destruction of the terrorist's home was part of the ongoing war against terror and its infrastructure, and was carried out in accordance with orders of the political echelon.
A statement issued by the security establishment said the demolition of the homes of militants "is a clear message to those seeking to harm citizens of Israel and security forces."
"The IDF will continue to operate in accordance with the orders of the political echelon, in cooperation with security agencies and will not hesitate to use all legal means at its disposal to strike at terrorists and those who help them, and to deter further attacks," the statement said.
The practice was earlier employed in the West Bank but had been halted in 2005 after the army said they had not deterred other attackers. The punitive action has caused much controversy in the past.
In recent weeks, Jerusalem has seen its worst bout of violence. Much of the violence has its root in a contested hilltop compound in Jerusalem's Old City.
Both Jews and Muslims revere the sacred site. But Palestinians see the increased visits by Israelis as a provocation.