The fatal stabbing of two young Israelis further heightened tensions as Palestinians were set on Tuesday to commemorate the 10th anniversary of the death of iconic leader Yasser Arafat.
Monday's violence began in Tel Aviv, where a Palestinian teenager from the northern West Bank stabbed a 20-year-old soldier who later died of his wounds in hospital. 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 a security guard shot and critically wounded him.
The bloodshed took place after months of clashes in and around annexed east Jerusalem, with the unrest spreading to Arab areas of Israel at the weekend after police shot dead a young Arab-Israeli during a routine arrest operation.
Events marking the 10th anniversary of Arafat's death have been cancelled in the Gaza Strip due to security concerns, but were expected to go ahead in the West Bank.
The Palestinian leader, who signed the 1993 Oslo peace accords with Israel but walked away from talks hosted by the US at Camp David in 2000, died aged 75 at a hospital in Paris in 2004. His death remains clouded in mystery, with some research indicating he may have been poisoned by polonium, a theory which is accepted by many Palestinians.
The deadly knife attacks were condemned by the United States and the European Union.
"It is absolutely critical that parties take every possible measure to protect civilians and de-escalate tensions," said State Department spokeswoman Jen Psaki.
The office of EU foreign affairs chief Federica Mogherini warned the situation could further deteriorate "in the absence of political perspective".
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 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.
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