The structure and electronic properties of different terminations of hematite (0001) and magnetite (111) surfaces upon submonolayer Fe adsorption were studied using the spin-polarized density functional theory (DFT) including the Hubbard correction term U (DFT+U). On both oxides the Fe atoms were adsorbed on the most stable iron and oxygen terminated surfaces. The results show that Fe atoms bind strongly both to hematite and magnetite surfaces, however, the binding is distinctly stronger at the oxygen than at the iron terminated surfaces. For both oxides and surface terminations the binding energy of the Fe decreases with increasing coverage, which indicates substantial repulsive interactions between Fe adatoms. On the hematite surface, the most stable sites for Fe adsorption are bulk continuation sites which result in formation of the Fe-rich terminations. On the magnetite surface, the bulk continuation site is favored only for Fe adsorption on the oxygen terminated surface while on the iron terminated one Fe adsorbs in a position closer to the surface iron layer. Submonolayer coverages of Fe modify substantially the surface electronic structure of the oxides and, depending on the termination, can change its character from half-metallic to insulating one, and vice versa.