A Palestinian man has been killed after he allegedly opened fire near an Israeli police station in occupied East Jerusalem, killing two and leaving at least six others wounded, according to police and witnesses.

The alleged drive-by attack occurred on Sunday at a light rail station near the Israeli police headquarters in Sheikh Jarrah, close to the line dividing mainly Palestinian East Jerusalem from the mostly Jewish western sector of the city.

Israeli police responded to the scene, and after a short pursuit, shot and killed the alleged attacker - a 39-year-old Palestinian man identified by his family as Musbah Abu Sbeih from the neighbourhood of Silwan in Jerusalem.

Two critically wounded victims, a 30-year-old police officer and a 60-year-old woman, later succumbed to their wounds, according to a spokesman at Jerusalem's Hadassah hospital.