The fuel injection system comprises a fuel injector controlled by commands of a control unit. The fuel injector comprises a metering servo valve having a control chamber provided with an outlet passage that is opened/closed by an open/close element that is axially movable. The open/close element is carried by an axial guide element that is separate from an armature of an electromagnet. The open/close element is held in the closing position by a spring acting through an intermediate body. In some instances, the strokes of the open/close element and of the armature are chosen so as to eliminate, upon closing of the servo valve, the rebounds of the open/close element subsequent to the first rebound. The control unit controls a fuel injection comprising a pilot fuel injection and a main fuel injection, via two distinct electrical commands, which are spaced apart by a dwell time such as to occur in an area of reduced variation of the amount of injected fuel. Therefore, the stability of operation of the fuel injection system increases as the dwell time varies.