One Israeli later died from his wounds and another man, who was apparently wounded by the police as they shot at the Palestinian assailants, also died later.
Police spokeswoman Luba Samri said the attack happened outside the city's Jaffa Gate, a popular spot for tourists visiting Jerusalem's walled Old City. She said police shot both assailants who were later identified as Palestinians in their early 20s from the West Bank. One died at the scene and the second later, in hospital.
Since mid-September, near-daily Palestinian stabbing, shooting and car ramming attacks have killed 20 Israelis and an American student. At least 120 Palestinians have died by Israeli fire in the same period, including 82 said by Israel to be attackers. The rest have been killed in clashes with Israeli security forces.
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Also today, the Israeli Shin Bet intelligence agency said it had uncovered "a wide terrorist infrastructure" of the militant Islamic group Hamas in the West Bank and Israel, directed from Gaza.
The agency said it arrested 25 suspected Hamas members who operated in the area of Abu Dis east of Jerusalem and in Bethlehem, in the West Bank. Shin Bet said the militants operated an explosives laboratory in Abu Dis, and planned to carry out suicide bombings in Israel.