The Israeli cabinet approved measures to make it easier for Israelis to carry weapons, after two separate attacks carried out by two Palestinians in Jerusalem over the past two days.
The attacks took place after an Israeli army raid in the occupied West Bank that killed nine people.
The new measures include depriving family members of an attacker of residency and social security rights.
The whole government is due to consider the measures on Sunday.
Prime Minister Benjamin Netanyahu had promised a “strong” and “rapid” response before the cabinet meeting.
The Israeli military also said it would boost troop numbers in the occupied West Bank.
“When civilians carry guns, they can defend themselves,” far-right National Security Minister Itamar Ben Gvir told reporters outside a hospital in Jerusalem.
The security cabinet said these measures would revoke the right to social security for “families of terrorists who support terrorism”.
The proposals are in line with those from Netanyahu’s far-right political allies, who allowed him to return to power last month.
This came after Israeli police said a 13-year-old Palestinian boy was behind a shooting in the Silwan neighborhood of Jerusalem on Saturday that seriously injured an Israeli and his son.
A spokesman for the Israeli police said earlier that the attacker ambushed five people, while they were on their way to pray, and that two of them were in “critical condition.” The Palestinian boy was shot by passers-by and is currently being held in a hospital.
In a separate shooting on Friday at a synagogue in East Jerusalem, seven people were killed and at least three others wounded as they gathered to pray at the start of the Jewish Sabbath. The gunman was shot dead at the scene.
Local media said the man behind Friday’s synagogue attack was a Palestinian from East Jerusalem.
Police have arrested 42 people in connection with the attack.
Israeli Police Commissioner Kobi Shabtai described the attack as “one of the worst attacks we have faced in recent years”.
Palestinian armed groups praised the attack, but none of them claimed responsibility for the attack.
Before the mini-cabinet meeting, Netanyahu called for calm and urged citizens to allow the security forces to carry out their tasks, while the army said that additional forces would be deployed in the occupied West Bank.
“I call on all Israelis again – do not take the law into your own hands,” Netanyahu said. He thanked many world leaders – including US President Joe Biden – for their support.
Tensions have escalated since nine Palestinians were killed during an Israeli military raid in Jenin, in the occupied West Bank, on Thursday.
This was followed by the firing of rockets into Israel from Gaza, and Israel responded with air strikes.
Since the beginning of January, 30 Palestinians – both militants and civilians – have been killed in the West Bank.
Palestinian President Mahmoud Abbas suspended security cooperation arrangements with Israel after Thursday’s raid in Jenin.
The Friday synagogue shooting coincided with Holocaust Remembrance Day, which commemorates the six million Jews and other victims murdered by the Nazi regime in Germany.
Ukrainian President Volodymyr Zelensky condemned the attack, saying one of the victims was a Ukrainian woman.
“Terrorism should have no place in today’s world – neither in Israel nor in Ukraine,” he said in a tweet.
British Foreign Secretary James Cleverly wrote on Twitter: “The attack on worshipers in a synagogue on Holocaust Remembrance Day and during Shabbat is appalling. We stand with our Israeli friends.”
The White House said President Joe Biden has spoken with Netanyahu and offered “all appropriate means of support.”
Shortly after the incident, Netanyahu visited the site, as did the controversial far-right national security minister, Itamar Ben Gvir.
The BBC’s Yolande Neal in Jerusalem says Ben Gvir has promised to restore safety on Israel’s streets, but there is growing anger that he has not yet done so.
A spokesman for UN Secretary-General Antonio Guterres said the latter was “deeply concerned about the current escalation of violence in Israel and the Occupied Palestinian Territories.”
“This is a moment to exercise maximum restraint,” UN spokesman Stephane Dujarric said.
On Saturday, the European Union expressed concern about the escalating tensions and urged Israel to use lethal force only as a last resort.
Josep Borrell, the EU’s foreign policy chief, said: “The EU fully recognizes Israel’s legitimate security concerns – as evidenced by the recent terrorist attacks – but it must be emphasized that lethal force should only be used as a last resort when absolutely unavoidable in order to protect spirits.”
Israel occupied East Jerusalem in the 1967 war. It considers the entire city its capital, although this is not recognized by the vast majority of the international community.
Palestinians view East Jerusalem as the future capital of a hoped-for independent state.