Heavy rainfall under the conditions of the changing climate has recently garnered considerable attention. The statistics on heavy daily rainfall offer vital information for assessing present and future extreme events and for clarifying the impacts of global climate variability and change, working to form a favorable background. By analyzing a set of large-ensemble simulations using a global atmospheric model, this study demonstrated that two different physical processes in global climate variability control the interannual fluctuations in the 99th- and 90th-percentile values of summertime daily rainfall (i.e., the potential amounts) on Kyushu Island in western Japan. The 90th-percentile values were closely related to large-scale horizontal moisture transport anomalies due to changes in the subtropical high in the northwestern Pacific, which was usually accompanied by basin-scale warming in the Indian Ocean subsequent to the wintertime El Niño events. The contributions of the sea surface temperatures over the northern Indian Ocean and the eastern tropical Pacific Ocean showed low-frequency modulations, mainly due to the influences of the global warming tendency and the interdecadal variability in the climate system, respectively. In contrast, tropical cyclone activity played a major role in changing the 99th-percentile value. The potentials of both the tropical cyclone intensity and the existence density fluctuated, largely owing to the summertime sea surface temperature over the tropical Pacific, which can be modulated by the El Niño diversity on interdecadal timescales.