The global behavior and escape rate of hot oxygen atoms around Mars and their response to different solar wind dynamic pressure (P _SW) conditions are investigated using a multidimensional time-dependent magnetosheath-ionosphere-exosphere (Msh-I-E) coupling model. Recently we reported that an increase in P _SW leads to a short-term increase in the escape rate of nonthermal oxygen using a one-dimensional (1-D) Msh-I-E model. The model used in the present paper is a multidimensional version of our previous 1-D model. For the exosphere model, we adopt a three-dimensional Monte Carlo approach above a 250-km altitude, while a time-dependent two-stream approach is employed below 250 km. The exosphere model is coupled with a two-dimensional resistive magnetohydrodynamic model of the magnetosheath-ionosphere interaction, assuming axial symmetry with respect to the Sun-Mars line. The results of the present model are consistent with the results of the 1-D model. The escape rate of hot oxygen for P _SW = 0.36 nPa is roughly twice that for P _SW = 1.43 nPa under steady state conditions. For nonstationary conditions, where P _SW is suddenly increased from 0.36 to 1.43 nPa, the escape rate is temporarily enhanced by a factor of 2.3 to 4.5 compared with that of the steady state case. The hot oxygen density is found to be less dependent on P _SW than is the escape rate.