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The Indian summer monsoon is influenced by numerous factors, including aerosol-induced changes to clouds, surface and atmospheric heating, and atmospheric circulation. Most previous studies assessing the effect of aerosols on monsoon rainfall have focussed on the local impact of aerosols on precipitation on monthly to seasonal timescales. Here, we show that desert dust aerosol levels over the Arabian Sea, West Asia and the Arabian Peninsula are positively correlated with the intensity of the Indian summer monsoon, using satellite data and models; a leadlag analysis indicates that dust and precipitation vary in concert over timescales of about a week. Our analysis of global climate model simulations indicates that by heating the atmosphere, dust aerosols induce large-scale convergence over North Africa and the Arabian Peninsula, increasing the flow of moisture over India within a week. According to these simulations, dust-induced heating of the atmosphere over North Africa and West Asia rapidly modulates monsoon rainfall over central India.