Tibetans fear China will eventually name a rival successor to the Dalai Lama, bolstering Beijing's control over Tibet, the territory it poured troops into in 1950 and has ruled ever since.

The man who calls himself a "simple Buddhist monk" celebrated in India, where he has lived since he and thousands of other Tibetans fled Chinese troops who crushed an uprising in their capital Lhasa in 1959.

The Dalai Lama says only his India-based office has the right to identify his eventual successor.

"I join 1.4 billion Indians in extending our warmest wishes to His Holiness the Dalai Lama on his 90th birthday," Indian Prime Minister Narendra Modi said in a statement, read at celebrations in the Himalayan hilltown where the Dalai Lama lives.

"He has been an enduring symbol of love, compassion, patience and moral discipline," he added.

China insisted Wednesday that it would have final say on who succeeds the Tibetan spiritual leader.

Modi's effusive support is significant.

India and China are intense rivals competing for influence across South Asia, but have sought to repair ties after a 2020 border clash.

- 'Cherish freedom' -

US Secretary of State Marco Rubio also said in a statement, read at the celebrations in India, that Washington was "committed to promoting respect for the human rights and fundamental freedoms of Tibetans".

"We support efforts to preserve Tibetans' distinct linguistic, cultural, and religious heritage, including their ability to freely choose and venerate religious leaders without interference," the statement added.

Taiwan's President Lai Ching-te -- who leads an island that China says is part of its territory and has threatened to use force to seize -- said in a statement read at the ceremony that the example set by the Dalai Lama "resonates with all who cherish freedom, democracy and respect for human rights".

Messages from three former US presidents were also broadcast.

"At a time when we see the forces of division tearing at the fabric of our common humanity... I'm grateful for your enduring efforts to build a better, kinder, more compassionate world," Bill Clinton said.

"The world is a troubled place, and we need your spirit of kindness and compassion and love more than ever," George W. Bush added.

Barack Obama wished a "very happy birthday to the youngest 90-year-old I know".

"It is humbling to realise that you've been a leader on the world stage for longer than I've been alive," Obama said, in his message to his "dear friend".

"You've shown generations what it means to practice compassion, and speak up for freedom and dignity," Obama added. "Not bad for someone who describes himself as a simple Buddhist monk."