The development of quantum computing or magnetic storage systems requires the search for magnetic nanostructures with multiple magnetic configurations with controllable quantum spin states. The study of the magnetic properties of metal oxide nanowires is of particular importance for the development of these technological implementations. The present work is devoted to an ab initio study of the magnetic properties of Mn and Mn oxide (MnO) nanowires on vicinal Au surfaces with different step edge geometries. The existence of ferromagnetic and antiferromagnetic configurations of Mn and MnO nanowires on vicinal Au surfaces was found. The effect of oxidations and surface geometry on the appearance of ferromagnetic or antiferromagnetic properties of the nanowire was revealed. The ground state of pure Mn nanowires was shown to be dependent on the surface structure. At the same time, the ground state of oxide Mn nanowires is antiferromagnetic on all studied vicinal surfaces and did not depend on the surface structure. We observed an increase in the exchange interaction energy in nanowires under surface oxidation. The exchange interaction between manganese atoms in MnO nanowires is much stronger than in pure Mn nanowires.