We obtain a new global a priori estimate for solutions of the Navier-Stokes-Poisson system. As a corollary, we establish the unique global solvability in critical spaces for the system in any dimension greater than 2. Furthermore, a decay result similar to that of the barotropic compressible Navier-Stokes system in the critical L²-based Besov space is given, under a certain additional regularity assumption concerning only the low frequencies of the data. This talk is based on a joint work with Raphaël Danchin (Université Paris-Est).