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The formation of intrinsic point defects in the N-sublattice of semi-insulating Mg-doped GaN crystals grown by the ammonothermal method (SI AT GaN:Mg) was investigated for the first time. The grown-in defects produced by the displacement of nitrogen atoms were experimentally observed as deep traps revealed by the Laplace transform photoinduced transient spectroscopy in the compensated <i>p</i>-type crystals with the Mg concentrations of 6 × 10¹⁸ and 2 × 10¹⁹ cm⁻³ and resistivities of ~10¹¹ Ωcm and ~10⁶ Ωcm, respectively. In both kinds of materials, three closely located traps with activation energies of 430, 450, and 460 meV were revealed. The traps, whose concentrations in the stronger-doped material were found to be significantly higher, are assigned to the (3+/+) and (2+/+) transition levels of nitrogen vacancies as well as to the (2+/+) level of nitrogen split interstitials, respectively. In the material with the lower Mg concentration, a middle-gap trap with the activation energy of 1870 meV was found to be predominant. The results are confirmed and quantitatively described by temperature-dependent Hall effect measurements. The mechanism of nitrogen atom displacement due to the local strain field arising in SI AT GaN:Mg is proposed and the effect of the Mg concentration on the charge compensation is discussed.