Israeli police have concluded that a Palestinian construction worker who killed three Israelis with a bulldozer in Jerusalem last 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.

Hosam Dwayyat 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 Dwayyat, 30, as a troubled man with a record of drug offences.

They insisted the family had been unaware of his intentions.

Rosenfeld said Dwayyat, 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 Israelis were given armed police protection to protest at the house occupied by about 20 relatives of Dwayyat 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 Jewish settlers in the West Bank, pointing out the Dwayyat home.

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

BULLDOZERS

Israel's attorney-general 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.

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 occupied 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.

Wednesday's attack was the first in the city since another Palestinian with Israeli residence rights in Jerusalem shot dead eight students at a seminary in Jewish west Jerusalem in March.

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 one senior aide to Olmert 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".

Israel's annexation of East Jerusalem and nearby areas is not recognised internationally and Palestinians are negotiating to have the capital of their future state in the city.