In a system, a starter includes a motor for rotatably driving an output shaft with a pinion and an actuator that shifts the pinion toward a ring gear to be engaged with the ring gear. A monitor unit monitors a rotational speed of the internal combustion engine. The rotational speed of the internal combustion engine drops after an automatic control for stop of the engine. When an engine restart request occurs with the rotational speed being within a preset range during the rotational speed of the internal combustion engine dropping by the automatic control for stop of the engine, a drive unit drives the actuator to shift the pinion toward the ring gear to be engaged with the ring gear. The drive unit rotatably drives the motor with the pinion being engaged with the ring gear to thereby crank the crankshaft.