Israeli Prime Minister Benjamin Netanyahu has announced a series of punitive steps against the Palestinians, including plans to beef up Jewish settlements in the occupied West Bank, in response to a pair of shooting attacks that killed seven Israelis and wounded five others.

The announcement on Saturday cast a cloud over a visit next week by US Secretary of State Antony Blinken and threatened to further raise tensions following one of the bloodiest months in the West Bank and east Jerusalem in several years.

Netanyahu's Security Cabinet approved the measures in the wake of a pair of shootings, including an attack outside an east Jerusalem synagogue on Friday night in which seven people were killed.

Netanyahu's office said the Security Cabinet agreed to seal off the attacker's home in preparation ahead of its demolition. It also plans to cancel social security and health benefits for the families of attackers, make it easier for Israelis to obtain weapons, and step up efforts to collect illegal weapons.

The announcement said that in response to public Palestinian celebrations over the attack, Israel would take new steps to "strengthen the settlements" this week. It gave no further details.

There was no immediate response from Washington. The Biden administration, which condemned the shooting, opposes settlement construction in east Jerusalem and the West Bank lands sought by the Palestinians for a future state. The topic is likely to be high on the agenda as Blinken arrives Monday for talks with Israeli and Palestinian officials.

The weekend shootings followed a deadly Israeli raid in the West Bank on Thursday that killed nine Palestinians, most of them militants. In response, Palestinian militants in the Gaza Strip fired a barrage of rockets into Israel, triggering a series of Israeli airstrikes in response. In all, 32 Palestinians have been killed in fighting this month.

It remains unclear whether the Israeli steps will be effective. The attackers in the weekend shootings, including a 13-year-old boy, both appear to have acted alone and were not part of organized militant groups.

In addition, Netanyahu could come under pressure from members of his government, a collection of religious and ultranationalist politicians, to take even tougher action. Such steps could risk triggering more violence and potentially drag in the Hamas militant group in Gaza.

"If it's even possible to put this violent genie back into the bottle, even for a little while, this would require the reinforcement and proper deployment of forces and carefully managing the crisis without being guided by the widespread calls for revenge," wrote Amos Harel, the defense affairs commentator for the Haaretz newspaper.

Friday's shooting, outside a synagogue in east Jerusalem, left seven Israelis dead and three wounded before the gunman was killed by police. It was the deadliest attack on Israelis in 15 years.

Authorities published the names of four of the victims. They included 14-year-old Asher Natan; Eli Mizrahi, 48, his wife Natali, 45; and Rafael Ben Eliyahu, 56. Funerals for some victims were scheduled for Saturday night.

Ella Sakovich, an aunt of Natali Mizrahi, said that her niece had been celebrating the Jewish sabbath with her husband and his father when they heard gunfire outside on Friday night.

"While eating, she and her husband wanted to help and went out of the house to treat the wounded; they shot both of them," Sakovich said in a statement released by Hadassah Hospital, where Natali Mizrahi worked serving food to patients.

In response to the shooting, Israeli police beefed up activities throughout east Jerusalem and said they had arrested 42 people, including family members, who were connected to the shooter.

But later Saturday, a 13-year-old Palestinian boy opened fire elsewhere in east Jerusalem, wounding an Israeli man and his son, ages 47 and 23, paramedics said. Both were fully conscious and in moderate to serious condition in the hospital, the medics added.

As police rushed to the scene, two passers-by with licensed weapons shot and overpowered the 13-year-old attacker, police said. Police confiscated his handgun and took the wounded teen to a hospital.

Blinken is expected to arrive in Israel on Monday. The Biden administration condemned Friday night's shooting and has called for calm on all sides, but given few details on how it expects to promote these goals.

The attacks pose a pivotal test for Israel's new far-right government.

Both Palestinian attackers behind the shootings on Friday and Saturday came from east Jerusalem.

Palestinian residents of east Jerusalem hold permanent residency status, allowing them to work and move freely throughout Israel, but they suffer from subpar public services and are not allowed to vote in national elections.

Residency rights can be stripped if a Palestinian is found to live outside the city for an extended period or in certain security cases.

Israel captured east Jerusalem, along with the West Bank and Gaza Strip, in the 1967 Mideast war. The Palestinians seek all three areas for a future independent state. Israel has annexed east Jerusalem in a step that is not internationally recognised and considers the entire city to be its undivided capital.

Israel's new firebrand minister of national security, Itamar Ben-Gvir, has presented himself as an enforcer of law and order and grabbed headlines for his promises to take even stronger action against the Palestinians.

AP