Israeli PM Naftali Bennett says security forces will have "full freedom" to act after an attack in Tel Aviv killed three Israelis.
Two were killed when a Palestinian opened fire on a bar in one of the city's busiest streets on Thursday night. A third died on Friday.
The attacker evaded a huge manhunt for hours, before being shot dead in a gunfight in nearby Jaffa.
Israel has been rocked by a wave of attacks which have killed 14 people.
In the latest, Raad Hazem, 28, from Jenin in the occupied West Bank, shot people at the Ilka bar on Dizengoff Street, a main thoroughfare full of restaurants and bars in the heart of Tel Aviv, before escaping.
More than 1,000 members of the Israeli police, army special forces and the Shin Bet intelligence service poured into the city centre to try to find him, as police warned residents to stay indoors.
Hazem was found hiding near a mosque in the port of Jaffa, about four miles (6km) away, and was killed in a shootout with counter-terrorism and security agents.
Speaking in Tel Aviv on Friday morning, Prime Minister Bennett said security forces would have free reign to deal with threats.
"There are not and will not be limits for this war. We are granting full freedom of action to the army, the Shin Bet [domestic intelligence agency] and all security forces in order to defeat the terror."
"Every murderer knows we will find them, everyone who helps a terrorist should know that they will pay a heavy price."
Shin Bet said Hazem had entered Israel illegally and had no known links to militant organisations.
Palestinian President Mahmoud Abbas condemned "the killing of Israeli civilians", warning that "the killing of Palestinian and Israeli civilians only leads to a further deterioration of the situation", the official Palestinian Wafa news agency said.
However, the Palestinian militant group Hamas, which controls the Gaza Strip, and Palestinian Islamic Jihad, praised the attack.
Israeli media reports say Hazem had been sitting outside Ilka bar for about 15 minutes before he opened fire at about 21:00 (18:00 GMT), sparking pandemonium.
"I was heading north and as we were passing by a bar shots started," Mark Malfiev, who was injured, told the BBC.
"I saw the window shattering, suddenly people started running and I felt a back pain," he said. "I did not know there was an injury. I was just walking and then I felt a lot of blood, I saw blood."
CCTV footage showed people drinking then suddenly dashing away at the moment of the attack, overturning chairs in the scramble to escape. Video from Dizengoff Street showed people running away as emergency vehicles streamed into the area, sirens wailing.
The two men killed at the bar were named as childhood friends Eytam Magini and Tomer Morad, both aged 27. A 35-year-old father-of-three, who was one of 12 people wounded, died in hospital on Friday.
US Secretary of State Antony Blinken condemned the attack, adding that Washington stood with Israel "resolutely in the face of senseless terrorism and violence".
Israel's security forces were already on a high state of alert after a spate of deadly attacks in recent days.
At the end of last month, five people were shot dead by a Palestinian gunman in an ultra-Orthodox Jewish suburb of Tel Aviv. Days earlier, six people were killed in two attacks by three Israeli Arabs in the northern city of Hadera and the southern city of Beersheba. All the perpetrators were shot dead.
It marks the deadliest period of attacks in Israel since 2006, with fears of further incidents in the lead-up to the rare convergence next week of the Muslim festival of Ramadan, the Jewish festival of Passover and the Christian festival of Easter.