The system comprises an injector controlled by commands of a control unit. The injector comprises a dosing 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 anchor of an electromagnet. The open/close element is held in the closing position by a spring acting through an intermediate body. Preferably, the strokes of the open/close element and of the anchor are chosen so as to eliminate, upon closing of the solenoid valve, the rebounds of the open/close element subsequent to the first rebound. The control unit controls an injection comprising a pre-injection and a main 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 system increases as said dwell time varies.