Sinha stated this while visiting the Buddhist leaders in the central town of Kandy.
Sinha called on both main leaders of the two Buddhist chapters in Kandy who wield considerable power in the Buddhist-majority island.
He said he was looking forward to build on the existing close friendship between the two South Asian neighbours extending to cultural and trade spheres.
Sinha has assumed duties at a time of strained relations between the two countries over the harassment of Indian fishermen by Sri Lankan Navy.
However, the Indian assistance in rebuilding the war-torn regions in the island has drawn appreciation.
India has spent large sums of money to build 50,000 homes for people displaced by the erstwhile ethnic conflict while helping the island improve its northern and eastern infrastructure from building railway tracks to creating educational facilities.
But Colombo's plan to dilute powers to the Tamil-dominated north that were granted by the India-backed 13A amendment to the Sri Lanka constitution still remains a major irritant in bilateral relations.
New Delhi has expressed apprehensions over Sri Lankan plans regarding the 13A which was a direct intervention by India in 1987 during the three-decade-long Sri Lankan Civil War, intended to resolve the Buddhist-majority nation's ethnic conflict with the minority Tamils.