Lakes existed on Mars later than 3.6 billion years ago, according to sedimentary evidence for deltaic deposition. The observed fluviolacustrine deposits suggest that individual lake-forming climates persisted for at least several thousand years (assuming dilute flow). But the lake watersheds’ little-weathered soils indicate a largely dry climate history, with intermittent runoff events. Here we show that these observational constraints, although inconsistent with many previously proposed triggers for lake-forming climates, are consistent with a methane burst scenario. In this scenario, chaotic transitions in mean obliquity drive latitudinal shifts in temperature and ice loading that destabilize methane clathrate. Using numerical simulations, we find that outgassed methane can build up to atmospheric levels sufficient for lake-forming climates, if methane clathrate initially occupies more than 4% of the total volume in which it is thermodynamically stable. Such occupancy fractions are consistent with methane production by water-rock reactions due to hydrothermal circulation on early Mars. We further estimate that photochemical destruction of atmospheric methane curtails the duration of individual lake-forming climates to less than a million years, consistent with observations. We conclude that methane bursts represent a potential pathway for intermittent excursions to a warm, wet climate state on early Mars.