Résumé : Valuable theoretical predictions of nuclear dipole excitations in the whole chart are of great interest for different nuclear applications, including in particular nuclear astrophysics. Here we extend our large-scale calculations of the E1 γ -ray strength function, obtained in the framework of the axially- symmetric-deformed quasiparticle random phase approximation (QRPA) based on the finite-range D1M Gogny force, to the calculation of the M1 strength function. We compare our QRPA prediction of the M1 strength with available experimental data and show that a relatively good agreement is obtained provided the strength is shifted globally by about 2 MeV and increased by an empirical factor of 2. Predictions of the M1 strength function for spherical and deformed nuclei within the valley of β stability as well as in the neutron-rich region are discussed. Its impact on the radiative neutron capture cross section is also analyzed.