We present results of defect formation energies and charge state thermodynamic transition levels of Mg and Te interstitials in MgTe wurzite structure. We use the generalized gradient approximation and local density approximation functionals in the framework of density functional theory for all calculations. The formation energies of the Mg and Te interstitials in MgTe for both the tetrahedral and hexagonal configurations were obtained. The Mg and Te interstitials in MgTe depending on the functional, introduced transition state levels that are either donor or acceptor within the band gap of the MgTe. The Te interstitial exhibit charge states controlled metastability, negative-U and DX centre properties. The Mg interstitial acts as deep or shallow donor and there is no evidence of acceptor levels found for the Mg interstitial.