Eight Israelis were injured when a gunman opened fire at a bus near Jerusalem's Old City early on Sunday.
The suspected Palestinian attack comes a week after violence flared up between Israel and militants in Gaza, leading to 49 deaths in Gaza.
Two of the victims were in serious condition, including a pregnant woman with abdominal injuries and a man with gunshot wounds to the head and neck, according to Israeli hospitals treating them.
The shooting happened as the bus waited in a parking lot near the Western Wall, the holiest site where Jews can pray.
Israeli police said forces were dispatched to the scene to investigate. Israeli security forces also pushed into the nearby Palestinian neighbourhood of Silwan pursuing the suspected attacker.
Later on Sunday, police said the suspected attacker turned himself in. Police did not immediately disclose details about the suspected attacker's identity.
The attack in Jerusalem followed a tense week between Israel and Palestinians in Gaza and the West Bank.
Last weekend, Israeli aircraft unleashed an offensive in the Gaza Strip targeting the militant group Palestinian Islamic Jihad (PIJ) and setting off three days of fierce cross-border fighting. PIJ fired hundreds of rockets to avenge the airstrikes, which killed two of its commanders and other militants. Israel said the attack was meant to thwart threats from the group to respond to the arrest of one of its officials in the occupied West Bank.
Forty-nine Palestinians, including 17 children and 14 militants, were killed, and several hundred were injured in the fighting, which ended with an Egyptian-brokered cease-fire. No Israeli was killed or seriously injured.
The Islamic militant group Hamas, which controls Gaza, stayed on the sidelines.
A day after the cease-fire halted the worst round of Gaza fighting in more than a year, Israeli troops killed three Palestinian militants and wounded dozens in a shootout that erupted during an arrest raid in the West Bank city of Nablus.
(With AP inputs)
