He made the offer during a virtual summit with his Sri Lankan counterpart Mahinda Rajapaksa, reports AP.
Buddhism is practiced by more than 70% of Sri Lanka's population, while most of India's people are Hindu.
India's External Affairs Ministry said the promotion will be through construction and renovation of Buddhist monasteries, capacity development, cultural exchanges, archaeological cooperation and reciprocal exposition of Gautam Buddha's relics.
India recently upgraded its airport in Kushinagar, an important Buddhist pilgrimage site in the northern Indian state of Uttar Pradesh, to receive international flights.
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India also plans to fly a Buddhist delegation from Sri Lanka on the inaugural flight soon.
The Buddhists believe that Buddha attained a transcendent state after his death in Kushinagar.