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.
'Situation could further deteriorate'
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.
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 and died in hospital after the attack, which marked the first time Israel's hedonistic commercial capital has been affected by the current wave of violence.
The attacker was identified as 17-year-old Nureddine Abu Hashiyeh from Askar refugee camp near Nablus.
Israel is struggling to contain the growing wave of violence which has gripped annexed east Jerusalem for the past four months and 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.
The unrest spread at the weekend 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.
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."