Mechanical distributor injection pump having cold-start acceleration

A high-pressure pump for supplying internal combustion engines with fuel includes a housing, on which a timing unit for displacing the point of injection is accommodated. The timing unit includes an injection timing piston having inlet bores, and a regulating slide, whose face facing a cold-start accelerator piston has a prestress force applied to it, is movably accommodated in the injection timing piston. A spring element, which is applied directly to the injection timing piston, as well as a spring assembly, which is independent of the spring element and accommodated on a carrier and act on the regulating slide, are positioned between the cold-start accelerator piston and the opposing face of the injection timing piston.