Abstract This study investigates the role that sea surface temperature (SST) variability plays in modulating the relationship between decadal-scale mean precipitation and monthly-scale extreme precipitation using the Australian Community Climate and Earth System Simulator Earth System model (ACCESS ESM1.5) climate model. The model large ensemble successfully reproduces the observed strong co-variability between monthly mean rainfall and wet extreme rainfall, defined as monthly rainfall totals above the 95th percentile. Removing SST variability in the ACCESS ESM1.5 model significantly weakens the co-variability between mean and wet extremes over most of the globe, showing that SSTs play a key role in modulating this co-variability. The study identifies Pacific and Atlantic SST patterns as the main drivers of the decadal scale co-variability in mean and extreme wet precipitation. On the other hand, observations and model results show that co-variability between mean and dry extremes is generally weaker than for wet extremes, with highly regional signals. Model experiments also show that SST variability plays a weaker role in modulating the co-variability between the mean precipitation and dry extremes as compared to wet extremes. These results suggest that stochastic atmospheric variability plays a stronger role in generating dry precipitation extremes compared SST forcing.