The Al Aqsa Martyrs' Brigades, the armed wing of Yasir Arafat's Fatah faction, said it shot George Khury, 20, as he was jogging late on Friday.
The group apologised on Saturday after it turned out the victim was the son of a prominent Arab-Israeli attorney, Elias Khury.
Israeli police, backed by a helicopter, launched an immediate manhunt for the attackers, who escaped in a getaway car.
"This attack is part of persistent efforts on the part of all Palestinian organisations and Yasir Arafat's Fatah to intensify terrorist activities against Israel," Israeli government spokesman Avi Pazner said.
The latest death took to 897 the number of Israelis killed during the current Palestinian uprising. Palestinian deaths during the same period stood at 3855.
In a separate incident, a Palestinian man attempted to stab an Israeli occupation border guard near the city's Damascus Gate.
Israeli radio said the guard opened fire, slightly wounding the man.