The official said at least one of the men was a “senior Fatah militant,” though he declined to provide any of their names.
Witnesses reported gunfire in the area after the blast.
Israel’s Channel 10 TV quoted Israeli military officials as saying Palestinian fighters fired an anti-tank rocket at the car.
Israel said it was not involved in any attack.
Hamas took control of the territory after heavy fighting with security forces loyal to Mahmoud Abbas, the Palestinian president, in June.