Prime Minister Ehud Olmert and Defense Minister Ehud Barak voiced support for demolishing the homes of Arab terrorists on Wednesday after a resident of east Jerusalem rammed a bulldozer into cars, buses and pedestrians on one of Jerusalem's busiest streets, killing three people and wounding at least 45 others - including a six-month-old baby girl - before being shot dead by security personnel. The three fatalities were identified as Jerusalem residents Jan Relevy, 68, Elizabeth Goren Friedman, 54, and Batsheva Unterman, 33 - the mother of the six-month-old baby. Goren Friedman and Unterman were buried late Wednesday night in the capital, and the details of Relevy's funeral were yet to be made public. The attack began at noon when Husam Taysir Dwayat, a 30-year-old resident of the southeast neighborhood of Sur Bahir, drove out of a nearby light rail construction site and plowed his Caterpillar vehicle into anything and anyone, first on Rehov Sarei Yisrael and then on Jaffa Road, overturning a No. 13 Egged bus, flattening half a dozen cars and leaving destruction and carnage in his wake. "People started screaming, 'He is running us over, he is running us over!'" said traffic policewoman Elinor Nahum, 22, who was the first to shoot and wound Dwayat after nearly being crushed herself. "He tried to run over anything that moved," said Sami Grossman, a paramedic with the Zaka rescue and recovery organization, who quickly ditched his motorcycle when the terrorist aimed his bulldozer at him and any other vehicles nearby. "I saw the bulldozer smash the car with its shovel. He smashed the guy sitting in the driver's seat," said Yaakov Ashkenazi, an 18-year-old yeshiva student. Dwayat, who managed to drive about 500 meters in his nearly 10-minute rampage, next took aim at the city bus, repeatedly picking it up in the air like a toy until it overturned on the curb. All this time, security officers had been shooting at the bulldozer, but most of the bullets were stopped by the driver's cab. An off-duty police officer climbed atop the vehicle and wrestled with the wounded terrorist, managing to shoot him. Then an off-duty soldier who had been riding his bike home joined the policeman and Dwayat, and repeatedly shot the east Jerusalem man. The soldier, who cannot be identified due to a court order, said the attacker was shouting, "Allahu Akbar." As hundreds of people fled in panic, an elite police commando team on motorcycles sped toward the tractor, and one of the officers jumped on the tractor and shot the assailant dead. "I saw the cars and buses strewn on the street, and realized that this was a terror attack," said police officer Eli Mizrahi, 28. "He started to drive like crazy and held the steering wheel, pressing against it, and started to race down the street," Mizrahi told reporters at the scene. "I loaded my weapon and shot to kill." Three Palestinian terrorist groups took responsibility for the attack: Fatah's Aksa Martyrs Brigades; the Galilee Freedom Battalion, which is suspected of being affiliated with Lebanon's Hizbullah; and the left-wing Popular Front for the Liberation of Palestine. Palestinian Authority President Mahmoud Abbas of Fatah condemned the attack. In contrast, the Hamas government in the Gaza Strip praised Dwayat. "We consider it as a natural reaction to the daily aggression and crimes committed against our people in the West Bank and all over the occupied lands," Hamas spokesman Sami Abu Zuhri told The Associated Press. Israel Police Insp.-Gen. David Cohen praised the security officials for their quick responses and said the attacker appeared to have acted alone. The assailant, a father of two with a criminal record, was employed as a bulldozer operator by an east-Jerusalem based construction company that is carrying out infrastructure work for the city's long-delayed light rail project, Jerusalem police spokesman Shmuel Ben-Ruby said. It was not immediately clear how Dwayat obtained his permit to operate a bulldozer in light of his criminal record. He received a two-year sentence in 2001 for raping a Jewish woman with whom he was romantically involved. Sometime after he was released form prison, he married an Arab woman. Jerusalem Mayor Uri Lupolianski, whose daughter was riding in a nearby bus but was not hurt, said that a major disaster had been averted since the driver did not get to the city's nearby Mahaneh Yehuda open-air market. "To our regret, the attackers do not stop coming up with new ways to strike at the heart of the Jewish people here in Jerusalem," Lupolianski said as he visited the wounded at Shaare Zedek Medical Center. "We need to send a strong message to our enemies," Lupolianski said, "The home of this terrorist should not remain standing, and I hope the prime minister will make the appropriate decision with regard to that. To my disappointment, we didn't do it the last time." Lupolianski was presumably referring to the last attack in Jerusalem at the Mercaz Harav Yeshiva. The home of the terrorist who killed eight students at the yeshiva was not destroyed. "We are seeing, as a result of the security barrier, that it's harder and harder for terrorists to bring explosives into the country," Lupolianski said. "So as a result, they're finding new and creative ways, as we saw today, to execute attacks against civilians." Olmert instructed Justice Minister Daniel Friedmann Wednesday to look into the legal issues involved in destroying Dwayat's home. At the same time, the prime minister directed Welfare and Social Affairs Minister Isaac Herzog to stop any National Insurance Institute payments to the family of the terrorist. While keen on taking measures aimed at deterring similar acts in the future, Israel made it clear that the incident would not impact the current negotiations with the Palestinians. "Israel will continue in its efforts to achieve peace with its pragmatic Palestinian neighbors, in spite of the efforts of extremists to torpedo the process", Foreign Ministry spokesman Aryeh Mekel said. He said that action by the international community was essential, and that Israel expected to hear a "clear and unequivocal condemnation" of the attack, along with clear action to isolate extremist elements. US President George W. Bush called Olmert soon after the attack to express his condolences, and UN Secretary-General Ban Ki-moon also condemned the attack. Israel sent a letter to the UN Security Council calling for a condemnation of the attack. In the past, Israel routinely destroyed the homes of terrorists, but stopped after an Israeli report concluded that the demolitions were largely ineffective. More than one-third of Jerusalem's 750,000 residents are Arabs. In contrast to Palestinians from the West Bank, Arab Jerusalemites have Israeli ID cards that allow them freedom of movement throughout Israel and the West Bank. Jerusalem police chief Cmdr. Aharon Franco conceded Wednesday that police had "no small difficulty" in dealing with the security threat posed by Arab resident of the city. Vice Premier Haim Ramon said Wednesday that the capital's Arab neighborhoods should be outside the West Bank security barrier. The bulldozer attack left Jaffa Road - already ripped up by construction work - looking like a battlefield with the overturned bus with its windows blown out and flattened cars, their hoods ripped up like a sardine can and stained with blood, the bloodied and dazed victims sitting or lying on the ground, and the plastic body bags lining the ground. "The bulldozer picked up the vehicles like a toy," eyewitness Yosef Spielman said. "It was like a nightmare." Abe Selig contributed to this report.