The three-site polarizable and flexible water potential employing the multistate empirical valence bond (MS-EVB) description for the electronic polarizability [A. E. Lefohn, M. Ovchinnikov, and G. A. Voth, J. Phys. Chem. 105, 6628 (2001)] has been modified for better reproduction of liquid water properties under ambient conditions. The improvement of the potential model was accomplished by (i) replacing the point charge distribution associated with the atomic interaction sites in the original model with a diffuse Gaussian charge distribution and (ii) reparameterizing the molecular geometry, components of electronic polarizability tensor, the Lennard-Jones parameters, and the widths of the Gaussian charge distribution. Static and dynamic properties, such as the intermolecular interaction energy, radial distribution function, diffusion constant, and dielectric constant, have been used in the model parameterization and the resulting model well reproduces the experimental data. A closely related rigid version of the model is also developed and compared with the flexible one. For computational efficiency, the extended Lagrangian algorithm for the electronic degrees of freedom has been implemented in the MS-EVB molecular dynamics simulation and utilized in the calculations. Relations between the new features of the potential model, such as the Gaussian charge distribution and the anisotropy in the electronic polarizability, and the liquid properties are established and discussed.