Israeli forces on Sunday prepared to demolish the family home of a Palestinian man who killed seven people near a synagogue, as part of measures to punish the relatives of attackers.

The security cabinet earlier agreed a slew of steps, including rescinding the rights to social security benefits of "the families of terrorists that support terrorism".

Prime Minister Benjamin Netanyahu's cabinet said the east Jerusalem home of Khayri Alqam, 21 – who was shot dead by police following Friday's attack – "will be sealed immediately ahead of its demolition".

Israel routinely demolishes the homes of Palestinians who kill Israelis, although the process requires prior notice to families and allows for an appeals process.

Dani Shenhar, a legal expert at Israeli rights group HaMoked, said sealing off the home overnight demonstrated the government's desire for "revenge against the families".

The measure was carried out "in complete disregard for the rule of law", he charged, adding that HaMoked would launch a protest with Israel's attorney general.

Netanyahu said on Sunday that revoking Israeli identity cards of the relatives of attackers was on the agenda of the weekly cabinet meeting.

The punitive measures announced are in line with proposals from Netanyahu's extreme-right political partners, whose support enabled him to return to power at the end of December.

They are likely to apply primarily to Palestinians with Israeli nationality, known as Arab-Israelis, and Palestinians with residency permits for annexed east Jerusalem.

Hours after the deadly shooting outside the synagogue in the settlement of Neve Yaacov, a 13-year-old Palestinian boy shot and wounded two Israelis just outside the walled Old City of east Jerusalem.

The boy blamed for the attack in the Silwan neighbourhood was shot and wounded at the scene and detained.

Another Palestinian hurt in prior clashes with Israeli forces in Silwan died from his wounds on Friday.

The mounting toll was described as a "death spiral" by Pope Francis, who referred to both Palestinians and Israelis killed.

"The death spiral that increases day by day only closes the few glimmers of trust that exist between the two peoples," the pontiff said on Sunday.

US Secretary of State Antony Blinken is expected in Jerusalem and Ramallah on Monday and Tuesday to discuss steps for de-escalation.

Palestinian president Mahmoud Abbas and Netanyahu are due to meet separately with Blinken, for talks that have taken on renewed urgency amid the latest bloodshed. (AFP)