A majority of the point defects in GaN that are responsible for broad photoluminescence (PL) bands remain unidentified. One of them is the green luminescence band (GL2) having a maximum at 2.35 eV which was observed previously in undoped GaN grown by molecular-beam epitaxy in Ga-rich conditions. The same PL band was observed in Mg-doped GaN, also grown in very Ga-rich conditions. The unique properties of the GL2 band allowed us to reliably identify it in different samples. The best candidate for the defect which causes the GL2 band is a nitrogen vacancy (VN). We propose that transitions of electrons from the conduction band to the +/2+ transition level of the VN defect are responsible for the GL2 band in high-resistivity undoped and Mg-doped GaN.