Functional tissue regeneration is required for the restoration of normal organ homeostasis after severe injury. Some organs, such as the intestine, harbour active stem cells throughout homeostasis and regeneration; more quiescent organs, such as the lung, often contain facultative progenitor cells that are recruited after injury to participate in regeneration. Here we show that a Wnt-responsive alveolar epithelial progenitor (AEP) lineage within the alveolar type 2 cell population acts as a major facultative progenitor cell in the distal lung. AEPs are a stable lineage during alveolar homeostasis but expand rapidly to regenerate a large proportion of the alveolar epithelium after acute lung injury. AEPs exhibit a distinct transcriptome, epigenome and functional phenotype and respond specifically to Wnt and Fgf signalling. In contrast to other proposed lung progenitor cells, human AEPs can be directly isolated by expression of the conserved cell surface marker TM4SF1, and act as functional human alveolar epithelial progenitor cells in 3D organoids. Our results identify the AEP lineage as an evolutionarily conserved alveolar progenitor that represents a new target for human lung regeneration strategies.