We represent an approach to calculate micromagnetic model parameters such as the tensor of exchange stiffness, Dzyaloshinskii-Moriya interaction (DMI), as well as spin-wave stiffness. The scheme is based on the fully relativistic Korringa-Kohn-Rostoker Green function (KKR-GF) technique and can be seen as a relativistic extension of the work of Lichtenstein et al. [J. Magn. Magn. Mater. 67, 65 (1987)]. The expression for Dzα elements of DMI differ from the expressions for Dxα and Dyα elements as the former are derived via second-order perturbation term of the energy caused by spin-spiral while the latter are associated with the first-order term. Corresponding numerical results are compared with those obtained using other schemes reported in the literature.