The system has a high-pressure pump having a number of mechanical pumping elements for pumping high-pressure fuel to a common rail; and a number of injectors communicating with the rail and activated to inject a quantity of fuel sequentially into the corresponding cylinders of the engine. Each pumping element has a delivery at least equal to the maximum draw of each injector, and is activated in phase with at least one of the injectors to minimize the variations in fuel pressure in the rail. Each pumping element may be activated by a cam, which may even have a segmented profile to effect a portion of the travel of the respective pumping element in phase with a corresponding injector.