Four Israelis were stabbed in separate attacks Monday, the first outside Jerusalem and the West Bank in 10 days, while a Palestinian teenager who tried to knife a soldier was shot dead.
Israeli border police also stormed a Palestinian university in the occupied West Bank, following more than a month of violence that has raised fears of a third Palestinian intifada, or uprising.
An Israeli in his seventies was left in serious condition after he was stabbed by a Palestinian in Netanya, 30 kilometres (18 miles) north of Tel Aviv.
The attacker was "neutralised", police said.
Earlier, three Israelis were stabbed in attacks near the central bus station in Rishon LeZion, about 10 kilometres (six miles) south of Tel Aviv, a police statement said.
The attacker, a 19-year-old Palestinian from Hebron in the West Bank, stabbed two people on the pavement and a third in a clothes store, the statement added.
The foreign ministry said one of the victims was an 80-year-old woman, while the country's medical service said two of the three Israelis stabbed were in severe condition.
The attacker was arrested by security forces after he was locked in the shop, police said.
The attacks were the first outside of the West Bank and Jerusalem since October 22, according to the Israeli authorities.
Nine Israelis, 68 Palestinians -- around half of them alleged attackers -- and an Arab Israeli have been killed in a wave of violence since the start of October.
The foreign ministry has reported 57 stabbing attempts, six car rammings and five shootings since the beginning of October.
The violence was originally focused in and around Jerusalem but the epicentre moved to Hebron over the past week.
The random nature of the attacks, and the fact that most of the assailants were apparently acting alone, has made it harder for Israeli security forces to react.
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Police also said they uncovered an explosive device when they searched a car on Monday near Hebron.
The last successful bomb attack in Israel was on a bus in Tel Aviv in November 2012, according to Israeli officials.
- Stabbing foiled -
Also on Monday, a 16-year-old Palestinian, Ahmed Abu El Rob, attempted to stab an Israeli soldier at a border crossing in the northern West Bank and was shot dead, police said.
A second Palestinian, allegedly an accomplice, was arrested.
Elsewhere, Israeli border police stormed a university in the town of Abu Dis after clashes with students protesting Israel's separation barrier and Palestinian deaths.
The clashes erupted after students from Al-Quds University gathered to demonstrate at the foot of the controversial barrier that separates Abu Dis from Jerusalem.
Israel says the barrier, which stretches inside the West Bank, is necessary for security, while Palestinians brand it an "apartheid wall".
At least one protester used an axe as a makeshift sledgehammer to strike the wall.
The students then pulled back into the campus and rained stones on border police who approached the gates.
Israeli forces retaliated by firing rubber bullets, tear gas and stun grenades before forcing open the gates of the university and going inside.
The number of wounded in the confrontation was not immediately clear.
But Palestinian medics said many people were hit by rubber bullets and injured in the upper parts of their bodies, while others suffered from smoke inhalation due to tear gas.