A three‐dimensional (3‐D) atomic oxygen corona of Mars is computed for periods of low and high solar activities. The thermal atomic oxygen corona is derived from a collisionless Chamberlain approach, whereas the nonthermal atomic oxygen corona is derived from Monte Carlo simulations. The two main sources of hot exospheric oxygen atoms at Mars are the dissociative recombination of O2+between 120 and 300 km and the sputtering of the Martian atmosphere by incident O+pickup ions. The reimpacting and escaping fluxes of pickup ions are derived from a 3‐D hybrid model describing the interaction of the solar wind with our computed Martian oxygen exosphere. In this work it is shown that the role of the sputtering crucially depends on an accurate description of the Martian corona as well as of its interaction with the solar wind. The sputtering contribution to the total oxygen escape is smaller by one order of magnitude than the contribution due to the dissociative recombination. The neutral escape is dominant at both solar activities (1 × 1025s−1for low solar activity and 4 × 1025s−1for high solar activity), and the ion escape flux is estimated to be equal to 2 × 1023s−1at low solar activity and to 3.4 × 1024s−1at high solar activity. This work illustrates one more time the strong dependency of these loss rates on solar conditions. It underlines the difficulty of extrapolating the present measured loss rates to the past solar conditions without a better theoretical and observational knowledge of this dependency.