Halide perovskites are a promising optical gain media for lasers. In this work, the phenomenon of random lasing is studied in the halide perovskite MAPbI3 single crystal at a temperature of 4 K and pico- or femtosecond pulsed optical pumping. Spectral, temporal, polarimetric, and threshold measurements facilitate isolating random lasing from the photoluminescence background. Spectral localization of the lasing lines points to defect-related states emission as the lasing origin. Time-resolved photoluminescence study shows that the random lasing is emitted as an ultrashort pulse with a duration below 10 ps, and the photoluminescence background as a long 100 ps afterglow. The mechanism of lasing in MAPbI3 halide perovskite is determined, which is ultrafast radiation from states associated with defects. The obtained information will make it possible to increase the efficiency of lasing in halide perovskites by controlled introduction of radiating states in the material transparency region.