We report a firt-principles study of the pressure dependence of electronic and the magnetic properties of Ga𝒳Mni1-𝒳N compounds (𝒳 = 0.25, 0.50 and 0.75) in wurtzite-derived structures. We use the full-potential linearized augmented plane wave method (FP-LAPW) within of the density functional theory framework. We found that, the lattice constant vary linearly with Ga-concentration. The magnetic moment changes for a critical pressure. At 𝒳= 0.75, a rather abrupt onset of the magnetic moment from 0 to 6.02 µB at Per = 26.50 GPa is observed. For 𝒳= 0.25 and 0.50 Ga concentrations, the magnetic moment increases gradually when the pressure decreases toward the equilibrium value. We study the transition pressure dependence to a ferromagnetic phase near the onset of magnetic moment for each Ga𝒳Mni1-𝒳N compounds. The calculation of the density of states with Ga concentration is carried out considering two spin polarizations. The results reveal that for 𝒳= 0.75 the compound behaves as a conductor for the spin-up polarization and that the density of states for spin-down polarization is zero at the Fermi level. At this concentration the compound presents a half metallic behavior; therefore this material could be potentially useful as spin injector. At high pressures P > Pcr the compounds exhibit a metallic behavior