Sustained stimulated emission under continuous-wave (CW) excitation is a prerequisite for new semiconductor materials being developed for laser gain media. Although hybrid organic-inorganic lead-halide perovskites have attracted much attention as optical gain media, the demonstration of room-temperature CW lasing has still not been realized. Here, we present a critical step towards this goal by demonstrating CW amplified spontaneous emission (ASE) in a phase-stable perovskite at temperatures up to 120 K. The phase-stable perovskite maintains its room-temperature phase while undergoing cryogenic cooling and can potentially support CW lasing also at higher temperatures. We find the threshold level for CW ASE to be 387 W cm-2 at 80 K. These results indicate that easily-fabricated single-phase perovskite thin films can sustain CW stimulated emission, potential at higher temperatures as well, by further optimization of the material quality in order to extend the carrier lifetimes