Israel’s prime minister has called on citizens with gun licences to arm themselves after the bloodiest attack in years in greater Tel Aviv, which marked the third such killings spree in the Jewish state in a week.

“What is expected of you, Israeli citizens? Vigilance and responsibility,” the country’s far-right leader, Naftali Bennett, said in a video statement on Wednesday evening. “Whoever has a gun licence, this is the time to carry it.”

Bennett, who spoke from his home where he is in quarantine after testing positive for Covid, had earlier said the country was facing a “new wave of terror”.

The back-to-back attacks have left Israelis and Palestinians bracing for further violence.

The defence minister, Benny Gantz, announced he had ordered 1,000 soldiers to bolster police forces, and Israel’s military presence in the Palestinian territories it occupies has been reinforced.

The bloodshed comes at a dangerous time. Next month, a rare convergence of Ramadan for Muslims, Passover for Jews and Easter for Christians is expected to raise tensions, with people off work and in the streets. Israel tightly controls access to Jerusalem’s holy sites for all three religions, which has previously led to confrontations.

Those holidays also precede a series of delicate anniversaries in the coming weeks. Some, such as Israeli independence day and the Palestinian Nakba commemoration of their expulsion, are decades old. Others are fresher, such as the one-year anniversary of the 11-day May conflict that killed more than 250 people in Gaza and 13 in Israel.

In the aftermath of Tuesday’s shooting rampage in Bnei Brak on the outskirts of Tel Aviv, one car’s white leather seats had been stained with blood, as were the front tiles of a nearby grocery shop, near multipacks of Coca-Cola bottles and a crisp packet stand.

The victims were a diverse mix – two Jewish ultra-Orthodox residents, Yaakov Shalom, 36, and Avishai Yehezkel, 29; two unnamed Ukrainians living in Israel as construction workers; and Amir Khoury, 32, a Christian Arab police officer who had engaged in a firefight with the attacker.

Police identified the perpetrator as Diaa Armashah, 27, a Palestinian from the occupied West Bank. He had arrived in Bnei Brak with an M-16 assault rifle and opened fire on cars, cyclists and balconies.

Amateur video footage showed a man wearing black walking into a street with a long gun as people ran away.

At one of the funerals on Wednesday, Ovadia Yehezkel said his brother, Avishai, had used his body to shield his two-year-old son in a stroller. “You cared for your son; you did not give up,” Ovadia said in a eulogy, according to the Times of Israel news outlet.

Israeli forces operating in the occupied West Bank on Wednesday arrested five Palestinians allegedly involved. The Palestinian Prisoner’s Club, a group that represents current and former Palestinian prisoners, said those arrested were Amarshah’s relatives.

Bnei Brak’s bloodshed brought the total death toll in Israel in recent days to 11, the highest number of people killed by militants in such a short period outside wartime in several years.

Last week, an attack in the southern city of Beersheba, in which four people were killed in a stabbing and car-ramming rampage, was carried out by an Arab citizen of Israel.

On Sunday, an Arab assailant, a resident of a town in the north of the country, shot and killed two police officers in Hadera, a city north of Tel Aviv, before he was gunned down by other officers.

Both those attacks were claimed by Islamic State, an organisation that is not known to have a large presence inside the country but which Israeli and Palestinian authorities fear could wield increased influence.

Amos Harel, a military and defence correspondent for Haaretz newspaper, said Tuesday’s attack – which he said may have been a “copycat” attack by a sympathiser inspired by last week’s attacks – was “Israel’s worst fear come true”.

“On three separate occasions, terrorists managed to reach the heart of cities inside Israel and carry out campaigns of slaughter unhindered,” he wrote. “None of the attacks were preceded by intelligence warnings. For now, the terrorists seem to be one step ahead of the security services, which still seem to be groping in the dark. Israelis’ sense of personal security has suffered a serious blow.”

He added: “In the coming days, we will likely see more stormy demonstrations, calls for vengeance and perhaps attacks on Palestinians and Israeli Arabs. Similar things happened last May during the Hamas-Israel war in the Gaza Strip.”

The Palestinian president, Mahmoud Abbas, who is based in the West Bank, issued a condemnation of the Tuesday night attack. “The killing of Palestinian and Israeli civilians will only lead to further deterioration of the situation, while we are all striving for stability,” Abbas said in a statement.

On Wednesday, Jordan’s King Abdullah II also condemned “violence in all its forms” in a meeting with visiting the Israeli president Isaac Herzog.

Earlier this week, Israel hosted a summit of Arab foreign ministers from Morocco, Egypt, the UAE and Bahrain in the Negev desert. Israel’s budding ties with former Arab foes, while continuing to control the lives of several million Palestinians living under occupation, have led to a sense of desperation and anger among Palestinians.