Israel Police have concluded that a Palestinian construction worker who killed three Israelis with a bulldozer in Jerusalemlast week acted alone and not as part of a militant organisation, a spokesman said on Sunday.

"(He) improvised the attack on his own," police spokesman Micky Rosenfeld said on a day when hundreds of officers were on hand to protect some 30 Israelis who demonstrated near the dead attacker's house to demand his family home be demolished, or in case the protest turned violent.

Husam Duwayit crushed cars and overturned a bus on Wednesday on one of Jerusalem's busiest streets. No major militant group claimed responsibility and relatives and neighbours described Duwayit, 30, as a troubled man with a record of drug offenses.

They insisted the family had been unaware of his intentions. Rosenfeld said Duwayit, who was shot dead at the scene, had shouted the Muslim slogan "Allahu akbar!" (God is greatest) and said police took that to indicate that he had intended to kill.

Bearing placards reading "Destroy the house" and "We want revenge", about 30 right-wing Israelis were given armed police protection to protest at the house occupied by about 20 relatives of Duwayit in a West Bank village annexed to Jerusalem by Israel.

Prime Minister Ehud Olmert's government has already taken legal advice paving the way for demolition - a tactic that has in the past provoked international condemnation of Israel.

"That is his house," said Baruch Marzel, a leader of settlers in the West Bank, pointing out the Duwayit home.

"We ... will come here again and again until his house and all the houses of the people who helped him will be destroyed."

"We demand it be done here and now," the activists said. "Every delay and postponement on this gives tailwind to terror. We must efface this house, and now."

Attorney General Menachem Mazuz ruled last week that a government move to destroy the house would be legal - but he also noted that it could face further legal challenges.

Defense Minister Ehud Barak on Friday ordered the Israel Defense Forces to issue injunctions calling to demolish the homes of two East Jerusalem men who had perpetrated terror attacks against Israeli civilians in Jerusalem this year.

The first home to be demolished was that of Duwayit. The second terrorist included in the injunction is Alaa Abu Dhaim who infiltrated the Mercaz Harav yeshiva in Jerusalem in March and gunned down eight students, also wounding many. Both perpetrators were killed by security forces during their respective attacks.

Israeli armoured bulldozers have demolished hundreds of Palestinian homes in the past decade on the grounds they have been built without permission. Palestinians complain that Israel unfairly denies building permits to Arabs in the West Bank and East Jerusalem, while encouraging Jews to build there.

In the past, the family homes of suicide bombers and other attackers have also been razed. This has been rarer following a sharp decline in such attacks and a 2005 challenge to the practice by human rights groups in Israel's Supreme Court.

Israel has effectively sealed off the Gaza Strip and occupied West Bank, building hundreds of kilometres (miles) of wall and fence around these areas to keep potential attackers out. But the roughly quarter of a million Palestinians given Jerusalem residency rights when Israel annexed East Jerusalem and neighbouring West Bank villages have freedom of movement.

That prompted Vice Premier Haim Ramon last week to suggest hiving off some Arab-populated areas of what Israel currently considers the municipality of Jerusalem. Olmert himself said Israel should destroy the homes of "every terrorist in Jerusalem."