First-principle total-energy calculations have been employed to investigate the epitaxial growth of manganese nitride (MnN) on the non-reconstructed GaAs (001)-(2 x 2) surface. Also, we have studied the surface nitridation process proposed by Gwo and Tokumoto. According to results, the surface nitridation generates a (3 x 3) flat surface that is composed by an array of missing N atomic rows along both [-110] and [110] directions. The initial stages of the epitaxial growth of MnN have been investigated by considering the adsorption and incorporation of Mn atoms. Calculations show that for 1/4 ML coverage the most favorable adsorption site of Mn induces an fcc configuration and for the Mn incorporation an hcp-2 arrangement. The surface formation energy (SFE) yields the adsorption of Ga adatoms at the hcp-2 site as a stable configuration; in addition, a surface with 3 Mn atoms replacing 3 Ga atoms of the 1st ML is stable for intermediate and As-rich conditions. When only one MnN ML is considered, three interfaces may be formed with 25%, 75% and 100% of Mn, which yield stable configurations showing the FM/AFM interface. A second MnN ML is considered; in this case, only one structure is stable, and an Mn/MnN interface is formed. Calculations show that the interface exhibits an FM/AFM coupling structure.