Abstract We present nowcasts of sudden heavy rains on meso-γ scales (2–20 km) using the high spatiotemporal resolution of a multiparameter phased-array weather radar (MP-PAWR) sensitive to rain droplets. The onset of typical storms is successfully predicted with 10-min lead time, i.e., the current predictability limit of rainfall caused by individual convective cores. A supervised recurrent neural network based on long short-term memory with 3D spatial convolutions (RN3D) is used to account for the horizontal and vertical changes of the convective cells with a time resolution of 30 s. The model uses radar reflectivity at horizontal polarization ZH and the differential reflectivity. The input parameters are defined in a volume of 64 × 64 × 8 km3 with the lowest level at 1.9 km and a resolution of 0.4 × 0.4 × 0.25 km3. The prediction is a 10-min sequence of ZH at the lowest grid level. The model is trained with a large number of observations of summer 2020 and an adversarial technique. RN3D is tested with different types of rapidly evolving localized heavy rainfalls of summers 2018 and 2019. The model performance is compared to that of an advection model for 3D extrapolation of PAWR echoes (A3DM). RN3D better predicts the formation and dissipation of precipitation. However, RN3D tends to underestimate heavy rainfall especially when the storm is well developed. In this phase of the storm, A3DM nowcast scores are found slightly higher. The high skill of RN3D to predict the onset of sudden localized rainfall is illustrated with an example for which RN3D outperforms the operational precipitation nowcasting system of Japan Meteorological Agency (JMA). Significance Statement Temporal extrapolation of radar observations is a means of nowcasting sudden heavy rains, i.e., forecasts with a few tens of minutes and a high spatial resolution better than 500 m. They are necessary to set up warning systems to anticipate damage to infrastructure and reduce the fatalities these storms cause. It is a difficult task due to the storm suddenness, restricted area, and nonlinear behavior that are not well captured by current operational observation and numerical systems. In this study, we use a new high-resolution weather radar with polarimetric information and a 3D recurrent neural network to improve 10-min nowcasts, the current limit of operational systems. This is a first and essential step before applying such a method for increasing the prediction lead time.