AbstractClimate impact models often require unbiased point‐scale observations, but climate models typically provide biased simulations at the grid scale. While standard bias adjustment methods have shown to generally perform well at adjusting climate model biases, they cannot overcome the gap between grid‐box and point scale. To overcome this limitation, combined bias adjustment and stochastic downscaling methods have been developed. These methods, however, are single‐site methods and cannot represent spatial dependence. Here we propose a multisite stochastic downscaling method that can be applied to bias‐adjusted climate model output for generating spatially coherent time series of daily precipitation at multiple stations, conditional on the driving climate model. The method is based on a transformed truncated multivariate Gaussian model and can also be used to downscale to a full field at finer‐grid resolution. An evaluation for stations across selected catchments in Austria demonstrates the good performance of the stochastic model at representing marginal, temporal and spatial aspects of daily precipitation, including extreme events.