The dynamical behavior of a thin film of ice Ih deposited on MgO(001) surface has been investigated both experimentally and theoretically. Incoherent neutron quasielastic scattering experiments, using uniform MgO powders, show that a quasiliquid water layer of monolayer thickness exists at T=265 K. The translational mobility of this layer, with a diffusion coefficient D-t=1.5x10(-5) cm(2) s(-1), is close to that of liquid water. At T=270 K, the thickness of the quasiliquid layer increases to about two layers, showing no appreciable change in the D-t value but an increase of the rotational mobility from 6x10(9) s(-1) to 1.2x10(10) s(-1). Classical molecular dynamics simulations are performed to determine the translational and orientational order parameters and diffusion coefficients of the supported ice film as a function of temperature within 190 and 270 K, and to compare the results with those obtained for bulk ice. It is shown that the whole supported ice film is much more disordered than bulk ice, with melting temperature around 235 K for the TIP4P potential used, while the melting temperatures of the outermost layer are nearly the same (around 220 K) for the supported film and bulk ice. Comparison of the values of the translational and orientational diffusion coefficients obtained in simulation and experiments displays a good agreement. Although the calculated value of the surface melting temperature is underestimated by 15% with respect to the experimental result, the present study indicates clearly the influence of the support on the melting process.