The response of mangroves to high rates of relative sea level rise (RSLR) is poorly understood. We explore the limits of mangrove vertical accretion to sustained periods of RSLR in the final stages of deglaciation. The timing of initiation and rate of mangrove vertical accretion were compared with independently modeled rates of RSLR for 78 locations. Mangrove forests expanded between 9800 and 7500 years ago, vertically accreting thick sequences of organic sediments at a rate principally driven by the rate of RSLR, representing an important carbon sink. We found it very likely (>90% probability) that mangroves were unable to initiate sustained accretion when RSLR rates exceeded 6.1 millimeters per year. This threshold is likely to be surpassed on tropical coastlines within 30 years under high-emissions scenarios.