As a token of sympathy, the Dalai Lama Trust is making contributions to the relief efforts of both the state and central governments, the Central Tibetan Administration statement said.
In letters to Prime Minister Manmohan Singh and Odisha Chief Minister Naveen Patnaik, the Nobel laureate, who is currently touring Mexico, expressed relief that the loss of life was minimal due to the efforts of the authorities.
Heavy rain brought by Cyclone Phailin that hit the state's coast Saturday night triggered floods in the districts of Balasore, Mayurbhanj, Jajpur, and Bhadrak and left thousands of people stranded.
More than one million people were affected when the water of major rivers and their tributaries in the region submerged low-lying areas and swamped homes.
The Tibetan exile administration is based in this northern Indian hill town.