In the framework of the density-functional theory we studied the atomic oxygen adsorption on the basal graphite surface at three imposed oxygen coverages 50, 25, 5.5% for three different adsorption sites, and also the dissolution of the atomic oxygen in graphite at one fixed coverage. Independently of the concentration, the most stable position of oxygen atoms is directly above a carbon-carbon bond (bridge), followed by the directly above a carbon atom position (top), and the directly above a hexagonal hollow (hex) site. Intercalating oxygen just below the surface layer, shows that dissoluted oxygen is more stable than adsorbed one.