We study the contemporaneous relationship between the intensity of the Indian Summer Monsoon (ISM) and runoff in the major rivers of the Aral Sea basin (Amudarya, Syrdarya) and some of their subcatchments. To this end, we use All-India rainfall (AIR) data, CRU surface observations of precipitation and temperature, ERA40 atmospheric data, and natural discharge data corrected for human interference. We show that there is a highly significant positive correlation between ISM intensity and Amudarya runoff. This finding cannot be explained by the spill-over of ISM precipitation over the Hindu Kush into the Amudarya basin. Instead, we suggest that the observed co-variability is mediated by tropospheric temperature variations due to fluctuations in the ISM intensity. These variations are known to be due to Rossby-wave propagation in response to condensational heating during monsoon precipitation. We hypothesise that the corresponding anomalies in surface temperatures imply anomalies in meltwater formation.