Police called the incident a terrorist attack. Hours after the rampage -- which ended when an off-duty police officer shot and killed 30-year-old Husam Taysir Dwayat -- Olmert met with government officials to discuss the possibility of destroying the man's home, The Jerusalem Post reported.
Israeli Defense Minister Ehud Barak also said that Israel should demolish the home of Dwayat, an Arab living in east Jerusalem.
Jerusalem Mayor Uri Lupolianski said he supported leveling the home as well.
"Only by destroying the terrorist's home will we be able to send out a clear message and prevent other youngsters who want to perpetrate terror attacks and kill Jerusalem residents from carrying out their plans," Lupolianski said at the scene.
Israeli Infrastructure, Trade and Labor Minister Eli Yishai called for legislation that would restrict movement of east Jerusalem Arabs and would permit the demolition of the homes of terrorists.