Break-up–related extrusive magmatism, imaged in reflection seismic data as seaward-dipping reflectors (SDRs), extends symmetrically along the volcanic margins of the Atlantic Ocean. Recent research found distinct along-margin variations in the distribution of SDRs, and abundance of volcanic material was found to be spatially linked to transfer fault systems. These segmented the propagating rift that later developed into the ocean, and are interpreted as rift propagation barriers. Based on these observations, we develop a numerical model, which shows that rift-parallel mantle flow and locally enhanced rates of volcanism are the result of delays in rift propagation and segmented opening. Our model suggests that segmentation is one of the major factors in the distribution and localization of rift-related extrusive magmatism. We conclude that in addition to mantle temperature and inherited crustal structures (e.g., weaknesses from previous rift episodes), rift propagation delay plays an important role in the distribution of extrusive volcanism at volcanic passive margins by controlling the mantle flow beneath the rift axis.