Short-range forecasts of precipitation fields are required in a wealth of agricultural, hydrological, ecological and other applications. Forecasts from numerical weather prediction models are often biased and do not provide uncertainty information. Here we present a postprocessing technique for such numerical forecasts that produces correlated probabilistic forecasts of precipitation accumulation at multiple sites simultaneously. The statistical model is a spatial version of a two-stage model that describes the distribution of precipitation with a mixture of a point mass at zero and a Gamma density for the continuous distribution of precipitation accumulation. Spatial correlation is captured by assuming that two Gaussian processes drive precipitation occurrence and precipitation amount, respectively. The first process is latent and governs precipitation occurrence via a truncation. The second process explains the spatial correlation in precipitation accumulation. It is related to precipitation via a site-specific transformation function, so to retain the marginal right-skewed distribution of precipitation while modeling spatial dependence. Both processes take into account the information contained in the numerical weather forecast and are modeled as stationary, isotropic spatial processes with an exponential correlation function. The two-stage spatial model was applied to forecasts of daily precipitation accumulation over the Pacific Northwest in 2004, at a prediction horizon of 48 hours. The predictive distributions from the two-stage spatial model were calibrated and sharp, and outperformed reference forecasts for spatially composite and areally averaged quantities.