Intricate branching patterns emerge in internal organs because of the repetitive presence of simple deformations in epithelial tissues. During murine lung development, epithelial cells in distal tips of a single tube require fibroblast growth factor (FGF) signals generated by their surrounding mesenchyme to form repetitive tip bifurcations. However, it remains unknown how the cells employ FGF signaling to convert their behaviors to achieve the recursive branching processes. Here we show a self-sustained epithelial regulatory system during the murine lung branching morphogenesis, mediated by extracellular signal-regulated kinase (ERK), which acts as a downstream driver of FGF signaling. We found that tissue-scale curvature regulates ERK activity in the lung epithelium using two-photon live cell imaging and mechanical perturbations. ERK is activated specifically in epithelial tissues with a positive curvature, regardless of whether the change in curvature was attributable to morphogenesis or artificial perturbations. Moreover, we found that ERK activation accelerates actin polymerization specifically at the apical side of cells, and mechanically contributes to the extension of the apical membrane, leading to a decrease in epithelial tissue curvature. These results indicate the existence of a negative feedback loop between tissue curvature and ERK activity beyond scale. We confirmed that this regulation was sufficient to generate the recursive branching processes by a mathematical model. Taken together, we propose that ERK mediates the curvature feedback loop underlying the process of branching morphogenesis in developing lungs.