Police said Palestinian gunmen shot an Israeli paramilitary border policeman near the Shuafat refugee camp near Jerusalem and that he died of his wounds at the scene.
A woman, also from the Israeli security services, received moderate to serious gunshot wounds in the same incident, a hospital spokeswoman said.
Israel Radio reported that a large number of police and soldiers were combing the area, searching for the gunmen.
In the second incident, settlers overpowered and shot dead two Palestinians who infiltrated a Jewish settlement in the occupied West Bank, an army spokeswoman said.
Israel radio said the Palestinians had stabbed two settlers at the Kfar Etzion settlement, not far from Bethlehem, before being shot, and a hospital spokeswoman in Jerusalem said the settlers' injuries were light to moderate.