The static dielectric constant of a water model (extended simple point charges, SPC/E) was evaluated by molecular dynamics simulations in the (N, V, E) ensemble for temperatures ranging from T = 324 K to 1278 K and densities from 0.257 g/cm3 to 1.1108 g/cm3. The dielectric constants calculated from fluctuations of the total dipole moment of the simulation box in the absence of an external field, and those obtained from the polarization response to an applied field were demonstrated to be consistent. Simulations within the pressure-temperature range (up to 500 MPa and 823 K) of available experimental data yield dielectric constant in very good agreement with experiment. It appears therefore that the SPC/E potential model can be used for the simulation of the dielectric properties of supercritical water and of aqueous solutions under supercritical conditions.