We present a reparametrization of an all-atom polarizable rigid model for water. The model is based on the earlier "Thole-type model" [J. Chem. Phys. 110, 4566 (1999)] and consists of a reparametrization of the two-body part of its potential energy surface from ab initio data. The new parametrization of the polarizable rigid model (TTM2-R) reproduces the structural pattern and absolute binding energies of the first few (n=2-6) water clusters to an impressive (<1%) accuracy with respect to the values obtained at the complete basis set (CBS) level of the second order perturbation theory. It also yields excellent agreement with the experimental second virial coefficient over the 423-773 K temperature range. The binding energies of the n=7-21 clusters are within 2-3% of the results with the newest version of the anisotropic site potential (ASP-W4). The new model produces a diffusion constant of 2.23 x 10(-5) cm(2) s(-1) for the liquid at 300 K and average dipole moments of 2.65 and 2.86 Debye for liquid (300 K) and ice Ih (100 K), respectively. The corresponding average internal energies are -11.21 kcal/mol/molecule for the liquid (300 K) and -14.69 kcal/mol/molecule for ice (0 K). The computed liquid radial distribution functions are in excellent agreement with experiment and the lattice constants for ice Ih are within 0.02 &ANGS; (<0.2%) from the experimentally obtained ones. The computed densities are 1.046 g/cm(3) for liquid water (300 K) and 0.942 g/cm(3) for ice Ih (0 K). To this end, TTM2-R is an ab initio based model that accurately reproduces both the cluster energetics and structures in addition to several bulk properties for water and ice Ih.