Monday's violence began in Tel Aviv where a Palestinian teenager from the northern West Bank stabbed a 20-year-old soldier, leaving him in critical condition. The assailant fled but was arrested.
Hours later, another Palestinian attacked three Israelis outside Alon Shvut settlement in the southern West Bank, killing a young woman and wounding two other people before he was shot dead by a security guard.
The bloodshed took place after months of clashes and unrest in and around annexed east Jerusalem which spread to Arab areas of Israel at the weekend after police shot dead a young Arab-Israeli during a routine arrest operation.
Since the summer, Israel has significantly increased police presence on the streets in a bid to rein in the unrest, but has been unable to stop a growing number of attacks by lone Palestinians, most of them in Jerusalem.
But Monday's violence was further afield.
"A car stopped at the hitchhiking stop at the entrance to Alon Shvut, the driver got out of the car and stabbed three civilians who were standing there," police spokeswoman Luba Samri said of the incident in the southern West Bank.
A woman of about 25 was killed and two men were lightly to moderately wounded, medics said. Police said all three were Jewish settlers.
Their attacker, who was identified as Maher Hamdi al-Hashlamon, was shot and seriously wounded by the settlement's security guard. He was taken to a Jerusalem hospital for treatment but died of his wounds shortly afterwards, police said.
Palestinian security sources said Hashlamon was from the southern city of Hebron.
TENSIONS REACH TEL AVIV
Earlier, a Palestinian teenager from a refugee camp in the northern West Bank stabbed an Israeli soldier outside a Tel Aviv train station before fleeing the scene. He was later arrested.
The soldier was critically wounded in the attack, which marked the first time Israel's hedonistic commercial capital has been affected by the current wave of violence.
"It was apparently an attack with nationalist motives. The suspect is a resident of the Nablus area," police spokeswoman Samri said.
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The attacker was identified as 17-year-old Nureddine Abu Hashiyeh from Askar refugee camp near Nablus. His father, Khaled, said he was a painter and decorator by trade and had left for Tel Aviv on Sunday.
The attacks came as Israel struggles to contain a growing wave of violence which has gripped annexed east Jerusalem for the past four months, but which has recently spread to Arab towns and villages inside the country.
Anger initially erupted in Jerusalem in early July over the murder of a Palestinian teenager by young Jewish extremists.
It has been fuelled by religious tensions at the flashpoint Al-Aqsa mosque compound, as well as by moves to expand settler presence in the occupied eastern sector of the holy city.
Since August, there have been four deadly Palestinian attacks in Jerusalem -- three of which were "hit-and-run terror attacks" which killed five Israelis -- and one attempted drive-by shooting.
All four perpetrators, who acted alone and came from east Jerusalem, were shot dead, sparking further unrest.
Since July, police have arrested some 900 Palestinians for public order offences in east Jerusalem and indicted around a third of them.
But at the weekend, the unrest spread after police shot dead a 22-year-old Arab-Israeli in Kufr Kana near the northern city of Nazareth, triggering a wave of rioting in Arab areas, some of which continued until early Monday.
Police claim the officers fired warning shots before shooting directly at him.
But relatives say Kheir Hamdan was killed "in cold blood", with CCTV images apparently contradicting the official version and showing an officer shooting at him as he was backing away from the scene.
Following two days of clashes, 24 Arab-Israelis -- 10 of them minors -- were in court on Monday on charges of stone-throwing and other public order offences, police said.
Prime Minister Benjamin Netanyahu vowed Sunday that anyone breaking the law would be "punished severely".
"We will not tolerate disturbances and riots. We will take determined action against those who throw stones, firebombs and fireworks, and block roads, and against demonstrations that call for our destruction."