When the rotational speed of an internal combustion engine is decreasing, the rate of decrease in engine rotational speed as well as the engine rotational speed are sensed. A command value dependent upon both the engine rotational speed and the speed decrease rate is generated when the engine rotational speed falls below a predetermined value, for regulating the opening of a control valve arranged in a bypass passage bypassing the engine throttle valve, to control the amount of intake air and, hence, the idling speed of the engine. Generation of the command value is terminated when the speed decrease rate falls below a predetermined threshold value preset in dependence upon engine rotational speed. Thus, the command value is outputted for a period of time which is not fixed in advance but which is controlled in dependence upon both engine rotational speed and the speed decrease rate, thereby enabling the rotational speed of the engine to be stabilized smoothly at the target idling rotational speed.