Many in-memory computing frameworks demand electronic devices with specific switching characteristics to achieve the desired level of computational complexity. Existing memristive devices cannot be reconfigured to meet the diverse volatile and non-volatile switching requirements, and hence rely on tailored material designs specific to the targeted application, limiting their universality. "Reconfigurable memristors" that combine both ionic diffusive and drift mechanisms could address these limitations, but they remain elusive. Here we present a reconfigurable halide perovskite nanocrystal memristor that achieves on-demand switching between diffusive/volatile and drift/non-volatile modes by controllable electrochemical reactions. Judicious selection of the perovskite nanocrystals and organic capping ligands enable state-of-the-art endurance performances in both modes - volatile (2 × 10 cycles) and non-volatile (5.6 × 10 cycles). We demonstrate the relevance of such proof-of-concept perovskite devices on a benchmark reservoir network with volatile recurrent and non-volatile readout layers based on 19,900 measurements across 25 dynamically-configured devices.