"I am deeply saddened to learn of the devastating earthquake... It has caused the tragic loss of many lives, numerous injuries, and extensive destruction to homes and property," the exiled leader said in a statement.

"I offer my prayers for those who have lost their lives and extend my wishes for a swift recovery to all who have been injured."

The powerful quake struck Tingri county, near the border with Nepal, killing at least 95 people according to Chinese state media.

The Dalai Lama was just 23 when he escaped the Tibetan capital Lhasa in fear for his life after Chinese soldiers eviscerated an uprising in 1959, crossing the snowy Himalayas into India. The Buddhist spiritual leader has never returned.

The Dalai Lama, now aged 89, stepped down as his people's political head in 2011, passing the baton of secular power to a government chosen democratically by some 130,000 Tibetans across the world.

Tenzin Lekshay, a spokesman of that government, said they were also "deeply saddened by the loss of lives and the extensive destruction of property" caused by the earthquake.

"Our heartfelt condolences go out to the grieving families," he said.

Tibetan Buddhists believe the Dalai Lama is the 14th reincarnation of the leader of an institution dating back six centuries, chosen by monks according to ancient Buddhist traditions.