Israeli security forces have taken up positions around the attacker's home
Israeli Defence Minister Ehud Barak has ordered the army to prepare to demolish the home of the Palestinian who killed three Israelis in Jerusalem.
The order follows advice by Attorney-General Menachem Mazuz that the proposed demolition could create legal difficulties, but would not be illegal.
An Israeli rights group has said such a move would be collective punishment.
B'tselem says it has written to Mr Mazuz demanding that he prevent the attacker's home from being demolished.
The group argues that the demolition would, as collective punishment, be illegal under international humanitarian law.
Hussam Dwayat went on the rampage at the wheel of a front-loader vehicle, or bulldozer, killing three people and wounding dozens before security personnel shot him dead.
On Thursday, Israeli Prime Minister Ehud Olmert said that Israel should destroy the homes of "every terrorist from Jerusalem".
The demolition of houses is a clear case of collective punishment, which violates the principle that a person is not to be punished for the acts of another
Mr Mazuz said in his legal opinion: "In light of repeated rulings over the years by the Supreme Court, it cannot be said that there is a legal objection… to the demolition of houses in Jerusalem, but the move would create considerable legal difficulties."
Mr Mazuz warned that apart from legal challenges in Israeli courts, a resumption of the practice of house demolitions could draw international condemnation.
He called for a detailed consideration of the circumstances surrounding each case by the internal security service, Shin Bet, the army and the justice ministry.
In February 2005, Israel abandoned the demolitions of homes of Palestinians involved in attacks against its citizens after human rights groups challenged the practice in Israel's Supreme Court.
Reports say about 20 people live in the home of the attacker Hussam Dwayat in the Sur Bahir area of East Jerusalem. They all insist that they had no prior knowledge of his intentions.
The Israeli authorities have said that Dwayat acted alone and was not connected to any Palestinian militant group.
In a statement about the anticipated demolition, rights group B'tselm said: "The declared objective of this policy is to harm innocent persons - relatives of suspected perpetrators, who are not accused of any criminal wrongdoing themselves.
"The demolition of houses is a clear case of collective punishment, which violates the principle that a person is not to be punished for the acts of another. Collective punishment is therefore illegal regardless of its effectiveness."
The group pointed to the findings of a committee appointed by a former chief of staff, Moshe Yaalon, as finding house demolitions did more harm than good to Israel's security.