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We have defined M cycles as modified form of Gleissberg cycles to study the quasi-periodic secular changes in sunspot activity. Using direct and proxy observations for more than 1200 years we have provided evidence for the influence of the above M cyles on the monsoon rainfall variability and occurrences of major droughts in India. The solar cycle averages of All Indian summer monsoon rainfall (AISMR) and probability of observation of below or above normal AISMR is found to show correlated variations with changes in amplitude of sunspot cycles during the years 1901-2018 AD. Major droughts in India show a preference to occur during minima and declining phases of the M cycles during the years 650-2018 AD . We could generally find low probability of occurrence of droughts in India during the medieval solar maximum epoch ( 1100-1250 AD) and during most of the prolonged sunspot minima periods including the Maunder minima. The evolution of mean Indian summer monsoon rainfall during 650-1900 AD is studied using proxy data from multiple sources with maxima during the 12th century and minima during 14th and 19th centuries. The association of Indian droughts with El-Nino and the possibilities of long term prediction of Indian summer monsoon rainfall variability will be also discussed