The system for rapidly reactivating a turbine engine of an aircraft includes an electrical machine that is DC powered from an on-board electrical power supply network. The system also includes a switch interposed between the on-board network and the electrical machine, an additional set including a plurality N electrical energy storage elements, and a control unit for controlling a device for discharging the storage elements and adapted to enable a series circuit including at least some of the N electrical energy storage elements to be connected in parallel with the on-board network so that when the rapid reactivation system is in operation the electrical machine is powered by a voltage level higher than the voltage level of its nominal characteristics.