The role of nonadditive interactions on the structure and dielectric properties of water is investigated at different temperatures using molecular dynamics. A new intermolecular potential is developed which contains an ab initio description of two-body additive interactions plus nonadditive contributions from both three-body interactions and polarization. Polarization is the main nonadditive influence, resulting in improved agreement with experiment for the radial distribution function, dielectric constant, and dipole moment. A comparison is also made with other widely used intermolecular potentials. The new potential provides a superior prediction of the dielectric constant and dipole moment. It also predicts the relative contribution of hydrogen bonding better than the SPC/E potential [Berendsen et al., J. Phys. Chem. 91, 6269 (1987)].