The Dalai Lama warned that China may choose its own Tibetan Buddhist as his successor after he dies.
The central government is considering the huge proposal that would divert water from Tibet to the Xinjiang region.
China and India also denied reports that 158 Indian troops were killed during recent Chinese military action in the tense border dispute.
India has resisted China's territorial ambitions, despite the aggressive noises from Beijing.
The backlash from Beijing over a bipartisan congressional visit to the Dalai Lama in India comes as relations between Donald Trump and Xi Jinping are warming.
They spare over neighboring allies, and are at odds over their shared border and the Dalai Lama.
The spiritual leader believes Trump will tone down his divisive promises once in office.
Americans Alex Lowe and David Bridges were filming a documentary series for NBC Sports when the avalanche struck.
Chinese border patrols lurk on the Tibetan side, ready to shoot anyone illegally crossing the pass.
Funded by the CIA, the hotel was meant to give Tibetan guerrillas a livelihood.
They hope the collapse of Chinese communism could lead to the return of a free Tibet.
Singer Yungchen Lhamo, who escaped Tibet on foot, is now helping mentally ill patients in the U.S. escape.
Death toll exceeds 3,200 as food and water shortages combined with aftershocks cause exodus from Kathmandu.
The government vowed safety improvements after dozens die last year, but tour operators say the measures aren't enough.
The White House said Obama had a "great relationship" with the Dalai Lama.