Speaking as the chief guest at the International Vesak Day celebrations in Colombo, Mr Modi said the ideologies of hate and their proponents in the region are closed to notion of dialogue and hence only open to causing death and destruction.
"The menace of terrorism in our region is a concrete manifestation of this destructive emotion," he said.
"The biggest challenge to sustainable world peace today is not necessarily from conflict between the nation states," he added and said it was from the mindsets, thought streams, entities and instruments rooted in the idea of hate and violence.
Mr Modi said he believes that "Buddhism's message of peace is the answer to growing arc of violence all over the world."
Lord Buddha's message is as relevant in the 21st century as it was two and a half millennia ago, Mr Modi told the audience which included Sri Lankan President Maithripala Srisena, Prime Minister Ranil Wickremesinghe, diplomats, politicians and several Buddhist leaders from across the world.
"Our region is blessed to have given to the world the invaluable gift of Buddha and his teachings," he said, adding that Buddhism and its various strands are deep seated in "our governance, culture and philosophy."
He said the countries of south, central, south east and east Asia are proud of their Buddhist links traced to the land of Buddha.
Prime Minister Modi assured India's support to Sri Lanka for the island's nation-building endeavours.
Mr Modi said that he believes that both India and Sri Lanka are at a moment of great opportunity in its relationship.
"You will find in India a friend and partner that will support your nation-building endeavours," he said and called on the two countries to uphold ideals of Lord Buddha and promote values of peace, inclusiveness and compassion in policies and conduct.