A fluid dispensing system comprising a pump (4) and a dispenser spray head comprising at least one nozzle through which fluid to be dispensed exits, the pump (4) comprising a stator (14) and a rotor (12) mounted in a chamber of the stator and rotatably displaceable with respect to the stator (14) around an axis of rotation (Ar) and axially along said axis (Ar), said axial displacement of the rotor in a first axial direction (A1) configured to effect a pump filling operation drawing in fluid via an inlet (8) into the stator chamber and in an opposite second axial direction (A2) configured to effect a dispensing operation expulsing the fluid in the chamber out of an outlet (10) of the pump. The outlet of the pump is positioned in the rotor and the dispenser spray head is fluidly connected to the outlet of the pump and is positioned at or adjacent an axial output end (19) of the rotor. The dispenser spray head is configured to dispense fluid at least partially in a radial direction (R) and encircling the axis of rotation.