We present a novel approach to construct pairwise site-site intermolecular interaction potentials from the results of ab initio quantum-mechanical modeling to be used in classical molecular simulations. In the present application, as a first step, we have carried out ab initio Car-Parrinello molecular dynamics (MD) simulations of liquid water to calculate the radial distribution functions (RDF) between all the pairs of nuclei. A second step involves use of the inverse Monte Carlo method, recently developed by us [Phys. Rev. E 52 (1995) 3730], to construct a full set of site-sire interaction potentials from the ab initio RDFs. The resulting three-site SPC-like water model, which reproduces the liquid structure obtained in the Car-Parrinello MD simulations, can be used as a potential function in classical molecular simulations. We have also found that there exist no pair potential for a rigid three-site water model which exactly satisfy the experimental water RDFs.