The invention is based on a fuel injection pump in which to supply a very rapid pressure rise in the interior of a fuel injection pump, a pressure valve controlling this pressure is modified such that upon cold starting of the engine, the pressure valve closes a bypass line at the feed pump and thus delivers all the fuel to the fuel injection pump. The closure is effected as a function of rpm and accordingly pressure, and also as a function of the engine operating temperature; in the fuel injection pump according to the invention, the rpm- and pressure-dependent diversion is performed by the adjusting piston of an injection adjuster. Thus, compared with the known cold-starting accelerating devices, one additional pressure limiting valve can be eliminated.