Earlier on Friday, retaliatory Israeli air strikes had hit Lebanon and the Gaza Strip, sparking fears of a broader conflict.
Israeli authorities said an Italian tourist was killed and five other Italian and British citizens were wounded when a car rammed into a group of tourists in Tel Aviv, Israel's commercial hub.
In a separate incident, two British-Israeli women were shot to death near a settlement in the occupied West Bank.
The spasm of violence in Israel and the West Bank heightened fears of an even more intense surge, with the rare convergence of the holy Muslim month of Ramadan, the Jewish Passover holiday and Easter currently under way.
Prime Minister Benjamin Netanyahu said he was calling up all reserve forces in Israel's border police, a paramilitary force usually deployed to suppress Palestinian unrest, "to confront the terror attacks".
The additional border police would be activated on Sunday and join other units that have recently been deployed in Jerusalem and Lod, a town in central Israel with a mixed Jewish and Palestinian population.
Israel had unleashed rare air strikes on Lebanon and bombarded the Gaza Strip on Friday morning, but later in the day there were signs that both sides were trying to keep the border hostilities in check.
The fighting subsided after dawn, and midday prayers at the Al-Aqsa Mosque in Jerusalem - a flashpoint for violence in recent days - passed peacefully.
The round of violence erupted after Israeli police raided the mosque earlier in the week, sparking unrest in the contested capital and outrage across the Arab world.
Militants fired an unusually large rocket barrage at Israel from southern Lebanon on Thursday - some of the heaviest and most serious cross-border violence since Israel's 2006 war with Lebanon's Hezbollah militants - as well as from Gaza.
In the Tel Aviv car-ramming late on Friday, the alleged attacker drove his vehicle into a group of civilians near a popular seaside park, police said.
Israel's rescue service said a 30-year-old Italian man was killed, while five other British and Italian tourists - including a 74-year-old man and a 17-year-old girl - were receiving medical treatment for mild to moderate injuries.
Police said they shot and killed the driver of the car and identified him as a 45-year-old Palestinian citizen of Israel from the village of Kafr Qassem.
A video circulating on social media showed the car hurtling along a sidewalk for several hundred metres before crashing out of control.
Italian Premier Giorgia Meloni's office expressed "closeness to the family of the victim" and "solidarity with the Israel for the vile attack". She identified the man killed as Alessandro Parini from Rome.
The shooting in the West Bank meanwhile killed the two sisters, who were in their 20s, and seriously wounded their 45-year-old mother near an Israeli settlement in the Jordan Valley, Israeli and British officials said.
No groups claimed responsibility for either attack. But the Hamas militant group that rules Gaza praised both incidents as retaliation for Israeli raids earlier this week on the Al-Aqsa mosque - the third-holiest site in Islam.
On Tuesday, police arrested and beat hundreds of Palestinians there, who responded by hurling rocks and firecrackers at officers.
Friday's air strikes on neighbouring Lebanon targeted Hamas militant sites, the Israeli military said, accusing the group of firing the nearly three dozen rockets that slammed into open areas and towns in northern Israel on Thursday.
There were no reports of serious casualties from the air strikes, but several people in the southern Lebanese town of Qalili, including Syrian refugees, said they were lightly wounded.
