The fuel premetering device has a valve controlled by an electromagnet and located between a delivery conduit of a high-pressure pump supplying fuel to a common rail, and a drain conduit for draining surplus fuel. The valve is normally closed by a spring, and the electromagnet is energized to open the valve in opposition to the spring. The electromagnet is energized by a current varying in response to the operating conditions of the engine, and which is varied by a control unit from zero, at which the valve is closed completely by the spring, to a predetermined value, at which the electromagnet opens the valve completely, so that premetering is self-adaptive. FIGS. 1 and 5