Rietveld refinement of monochromatic synchrotron x-ray powder diffraction data was used to study the evolution of octahedral tilting in the orthorhombic NaMgF3 perovskite under pressure. Hydrostatic pressure conditions were ensured up to 16 GPa using helium as a pressure medium. The tilting angles of MgF6 octahedral framework were observed to increase with increasing pressure. The compression mechanism was observed to be dominated by the shortening of the octahedral Mg-F bond below 6 GPa, and then controlled by the increase of the octahedral tilting above 12 GPa. The bulk modulus of NaMgF3 was estimated as 76.0 ¿ 1.1 GPa. A phase transition was observed at about 19.4 GPa in a separate run when silicone oil was used as pressure medium, and this high-pressure phase could be rationalized in term of a post-perovskite structural model.