The distal lung contains terminal bronchioles and alveoli that facilitate gas exchange. Three-dimensional in vitro human distal lung culture systems would strongly facilitate the investigation of pathologies such as interstitial lung disease, cancer and coronavirus disease 2019 (COVID-19) pneumonia caused by severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2). Here we describe the development of a long-term feeder-free, chemically defined culture system for distal lung progenitors as organoids derived from single adult human alveolar epithelial type II (AT2) or KRT5⁺ basal cells. AT2 organoids were able to differentiate into AT1 cells, and basal cell organoids developed lumens lined with differentiated club and ciliated cells. Single-cell analysis of KRT5⁺ cells in basal organoids revealed a distinct population of ITGA6⁺ITGB4⁺ mitotic cells, whose offspring further segregated into a TNFRSF12A^hi subfraction that comprised about ten per cent of KRT5⁺ basal cells. This subpopulation formed clusters within terminal bronchioles and exhibited enriched clonogenic organoid growth activity. We created distal lung organoids with apical-out polarity to present ACE2 on the exposed external surface, facilitating infection of AT2 and basal cultures with SARS-CoV-2 and identifying club cells as a target population. This long-term, feeder-free culture of human distal lung organoids, coupled with single-cell analysis, identifies functional heterogeneity among basal cells and establishes a facile in vitro organoid model of human distal lung infections, including COVID-19-associated pneumonia.