Hybrid organic–inorganic perovskites have emerged as promising gain media for tunable, solution-processed semiconductor lasers. However, continuous-wave operation has not been achieved so far1–3. Here, we demonstrate that optically pumped continuous-wave lasing can be sustained above threshold excitation intensities of ~17 kW cm–2 for over an hour in methylammonium lead iodide (MAPbI3) distributed feedback lasers that are maintained below the MAPbI3 tetragonal-to-orthorhombic phase transition temperature of T ≈ 160 K. In contrast with the lasing death phenomenon that occurs for pure tetragonal-phase MAPbI3 at T > 160 K (ref. 4), we find that continuous-wave gain becomes possible at T ≈ 100 K from tetragonal-phase inclusions that are photogenerated by the pump within the normally existing, larger-bandgap orthorhombic host matrix. In this mixed-phase system, the tetragonal inclusions function as carrier recombination sinks that reduce the transparency threshold, in loose analogy to inorganic semiconductor quantum wells, and may serve as a model for engineering improved perovskite gain media.