Abstract In this paper we present steady-state RMHD simulations that include a mass-load term to study the process of jet deceleration. The mass-load mimics the injection of a proton-electron plasma from stellar winds within the host galaxy into initially pair plasma jets, with mean stellar mass-losses ranging from 10−14 to 10−9 M⊙ yr−1. The spatial jet evolution covers ∼500 pc from jet injection in the grid at 10 pc from the jet nozzle. Our simulations use a relativistic gas equation of state and a pressure profile for the ambient medium. We compare these simulations with previous dynamical simulations of relativistic, non-magnetised jets. Our results show that toroidal magnetic fields can prevent fast jet expansion and the subsequent embedding of further stars via magnetic tension. In this sense, magnetic fields avoid a runaway deceleration process. Furthermore, when the mass-load is large enough to increase the jet density and produce fast, differential jet expansion, the conversion of magnetic energy flux into kinetic energy flux (i.e., magnetic acceleration), helps to delay the deceleration process with respect to non-magnetised jets. We conclude that the typical stellar population in elliptical galaxies cannot explain jet deceleration in classical FRI radio galaxies. However, we observe a significant change in the jet composition, thermodynamical parameters and energy dissipation along its evolution, even for moderate values of the mass-load.