Abstract Ultrafast laser pulses provide unique tools to manipulate magnetization dynamics at femtosecond timescales, where the interaction of the electric field usually dominates over the magnetic field. Recent proposals using structured laser beams have demonstrated the possibility to produce regions where intense oscillating magnetic fields are isolated from the electric field. In these conditions, we show that technologically feasible tesla-scale circularly polarized high-frequency magnetic fields induce purely precessional nonlinear magnetization dynamics. This fundamental result not only opens an avenue in the study of laser-induced ultrafast magnetization dynamics, but also sustains technological implications as a route to promote all-optical non-thermal magnetization dynamics both at shorter timescales – towards the sub-femtosecond regime – and at THz frequencies.