Increases in sea level are a threat to seaward fringing mangrove forests if levels of inundation exceed the physiological tolerance of the trees; however, tidal wetlands can keep pace with sea level rise if soil surface elevations can increase at the same pace as sea level rise. Sediment accretion on the soil surface and belowground production of roots are proposed to increase with increasing sea level, enabling intertidal habitats to maintain their position relative to mean sea level, but there are few tests of these predictions in mangrove forests. Here we used variation in sea level and the availability of sediments caused by seasonal and inter-annual variation in the intensity of La Nina-El Nino to assess the effects of increasing sea level on surface elevation gains and contributing processes (accretion on the surface, subsidence and root growth) in mangrove forests. We found that soil surface elevation increased with mean sea level (which varied over 250 mm during the study) and with turbidity at sites where fine sediment in the water column is abundant. In contrast, where sediments were sandy, rates of surface elevation gain were high, but not significantly related to variation in turbidity, and were likely to be influenced by other factors that deliver sand to the mangrove forest. Root growth was not linked to soil surface elevation gains, although it was associated with reduced shallow subsidence, and therefore may contribute to the capacity of mangroves to keep pace with sea level rise. Our results indicate both surface (sedimentation) and subsurface (root growth) processes can influence mangrove capacity to keep pace with sea level rise within the same geographic location, and that current models of tidal marsh responses to sea level rise capture the major feature of the response of mangroves where fine, but not coarse, sediments are abundant.