Israel’s vice premier is calling on Jerusalem to move its West Bank separation barrier to exclude outlying Arab neighborhoods, including the home district of a Palestinian man who killed three Israelis in a bulldozer rampage through the city center Wednesday.

Speaking to Israel's Army Radio station, Vice Premier Haim Ramon added Israel should strip people in these Palestinian districts of their Israeli residency rights.

In Wednesday's attack, the assailant, Hussam Dwayat, 30, drove a massive construction vehicle in a bloody rampage — ramming buses, crushing cars and targeting pedestrians. Three people died and dozens were wounded before security personnel climbed onto the vehicle and shot him to death. The infant child of one of the dead was recovered unharmed under the seat of an overturned bus.

Three Palestinian militant groups claimed responsibility for the attack but Israeli officials said they believe Dwayat acted alone.

No possible motive was provided though city officials confirmed that an order to demolish Dwayat's home was issued in 2005 on grounds that it was built illegally. Dwayat won a stay in court, but was ordered to pay tens of thousands of dollars in fines. Many Palestinians in Jerusalem build illegally, saying it's difficult for them to obtain permits from the Israeli authorities.

"Everyone is in shock," a family friend told the BBC.

Palestinian leader Mahmoud Abbas condemned the attack saying Thursday, "We want peaceful solutions through negotiations."

Abbas said President Bush phoned him just hours after the deadly rampage to "support" peace negotiations between Palestinians and Israelis. He also said that Palestinian and Israeli delegations will have a meeting in Washington "in the coming days," but provided no details.

Still, Wednesday's attack raised new questions about the future of the city and the government's policy toward Jerusalem's estimated 250,000 Palestinian residents, who make up about one-third of the total population.

Israel captured Jerusalem's eastern sector from Jordan in the 1967 Mideast War and annexed it to its capital. In Israeli-Palestinian peace talks, the Palestinians demand control over east Jerusalem, as their future capital. Israel rejects that idea, but Israeli Prime Minister Ehud Olmert and Ramon have signaled willingness to give up some Arab neighborhoods. Some Israeli hard-liners object to any changes in Jerusalem's boundaries.

Those boundaries had been redrawn by Israel after the 1967 war, by including what until then had been West Bank villages and thus dramatically increasing the land size of the city.

Dwayat, the assailant, was a resident of Sur Baher, one of those eastern areas that became part of Jerusalem in 1967. Ramon said Sur Baher and other outlying Palestinian neighborhoods "were never in Jerusalem."

"They were annexed in 1967 and we call them Jerusalem, even though there is not one Jerusalemite there. No Israeli goes near them," he said.

"It would be much more difficult to carry out attacks like these and 50,000 Palestinians who live in those two neighborhoods would not be able to reach Jerusalem so easily if they didn't have blue (Israeli) identity cards," he said.

The separation barrier has already cut off several Arab neighborhoods of Jerusalem, with tens of thousands of residents, from the city. Israel says the barrier is only meant to keep Palestinian militants out.

However, critics say the route of the barrier is largely determined by demographic considerations — to include the largest possible land area but exclude the largest possible number of Palestinians.

In another development, Palestinian militants fired a rocket at Israel Thursday afternoon, violating a June 19 truce, the military said. No one was hurt, but Israel's Defense Ministry decided to close Gaza crossings on Friday in response, cutting off the flow of vital supplies.

Wednesday's Jerusalem attack also drew attention to the uneasy relationship between Jews and Arabs in Jerusalem, threatening both Israelis' sense of security and Palestinians fragile status in the city.

At the site of the attack, construction crews were back on the job, working on a railway project. Rafael Greenbaum, a 63-year-old Jewish resident of the city, said he was still jittery.

"I was just thinking about what happened here," he said. "And I said to myself 'just like it happened to someone else yesterday. It could happen to me today."'

The vast majority of Jerusalem's Palestinians are not Israeli citizens. But unlike the Palestinians in the West Bank, they have Israeli residency rights, allowing them to work and move freely throughout the country and giving them social benefits. Many work in construction. Meron Benvenisti, former deputy mayor of Jerusalem from 1967 to 1979, said he believes the vast majority of Palestinians in the city value the benefits linked to Jerusalem residency.

"The majority cherish their status. They would not try this (such an attack)," he said. "There is no way you can generalize, but the majority of east Jerusalemites would like the status quo to continue."

In a preliminary reaction to the attack, the Israeli parliament gave initial approval to a bill that would strip the residency rights of the families of Palestinian attackers.

Olmert and other officials were also considering whether to demolish the home of the attacker.

The practice was halted by Israel in 2005 after military officials determined that wrecking the homes of Palestinian militants did not work as a deterrent. Officials said Olmert, Defense Minister Ehud Barak and Foreign Minister Tzipi Livni all favored reinstituting demolitions.

Olmert's spokesman, Mark Regev, said officials were exploring the legalities of possible responses, such as home demolitions or revoking residency rights of attackers' families. He said no decisions had yet been made.

Apart from a gun attack in March, Jerusalem has seen relatively little violence in the last three years. Since the start of 2008, across Israel and the occupied territories, 29 Israelis have been killed in violence linked to the conflict as have more than 400 Palestinians, the BBC reported.

Click here to read more from the BBC.

The Associated Press contributed to this report.