To reduce the construction expense and the space required for a fuel injection pump for supplying a plurality of cylinders of an engine, in particular an internal combustion engine having externally supplied ignition, a fuel injection pump including a drive shaft with a single common cam drives a plurality of pump plungers. The supply quantity is controlled via a rotary slide and a subsequent common distributor delivers the fuel to the injection nozzles at the injection sites of the engine. The quantity of fuel injected is effected by an electrically controlled valve seated in a relief line that branches off downstream of the rotary slide, which by closure of the relief line determines the injection phase.