The critical temperature TC of ferromagnetic LaxSr_1−xMnO₃ (LSMO) can be controlled by distorting the crystal structure, as was reported by Thiele et al (2007 Phys. Rev. B 75 054408). To confirm these findings theoretically, we investigate the electronic as well as the magnetic ground state properties of La_2/3Sr1/3MnO₃ as a function of tetragonal lattice distortions, using a multiple-scattering Green function method. Within this approach, we calculate exchange coupling constants as well as the phase transition temperature from first principles. Comparing our findings with those for La_2/3Sr1/3CoO₃ (LSCO), we find that the decrease of TC is much stronger in LSMO than in LSCO. Our findings can be explained by the electronic structures and are also in accordance with the experiment. The computed decrease of T_C with distortion is smaller than observed experimentally, a result that corroborates the importance of phonon contributions.