The pump includes a stator and a rotor having an impeller in which a fluid duct passes. An axial balancing device arranged on this wheel includes a rear balancing chamber and a passage arranged between the wheel and the stator, enabling evacuation of fluid from the fluid duct to the balancing chamber. The pressure of fluid in the balancing chamber compensates the pressures exerted by the fluid on the rest of the rotor allowing axial balancing of the rotor. The passage includes an upstream nozzle and a downstream nozzle, as well as an intermediate annular chamber, arranged between walls of the wheel and of the stator, the intermediate chamber being arranged downstream of the upstream nozzle and upstream of the downstream nozzle.