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A Palestinian man stabbed and killed two people in Jerusalem's Old City on Saturday before police shot him dead, officers said, amid an uptick in violence in the city and occupied West Bank.
Palestinian militant group Islamic Jihad issued a statement claiming the attacker as one of its members.
"The terrorist approached a group of Jews, whipped out a knife and began stabbing," police spokesman Micky Rosenfeld said.
One woman was in a critical condition after the assault and a toddler was lightly injured, police added.
On Sunday, less than 12 hours after the deadly attack, a Palestinian man stabbed and wounded an Israeli teenager in Jerusalem and was then shot dead by police, authorities said.
Police spokeswoman Luba Samri said the victim was taken to hospital in moderate condition and that police "saw the terrorist holding a knife, shot and neutralized him."
Violence has risen in East Jerusalem and West Bank in recent weeks. Though not at the levels of previous Palestinian uprisings or "Intifadas", it has raised Israeli fears of a greater escalation.
Israeli police and Palestinians have clashed frequently at East Jerusalem's al-Aqsa mosque compound, Islam's third holiest site, and at other parts of the city.
Prime Minister Benjamin Netanyahu was due to convene an emergency meeting with security officials later on Sunday, his office said, and a security cabinet meeting on Monday.
On Thursday, an Israeli couple was shot dead while their four children were in the car in a suspected Palestinian drive-by attack near a West Bank Jewish settlement.