He said he had received a call on Saturday from Tibet. “‘Please don’t ask us to stop,’” was the caller’s request. The Dalai Lama promised he would not, even though he said he expected the Chinese authorities to put down the protests with force.

“Now we really need miracle power,” he said, and then laughed. “But miracle seems unrealistic.”

As he entertained questions for over an hour here inside a temple in the lap of snow-capped Himalayas, the limits of his influence, and even his “middle path” message of freedom for Tibetans, rather than total independence for Tibet, came into sharp relief, as thousands of mostly young Tibetan exiles raised a chorus of stridently anti-Chinese slogans and called for secession.

“We the young people feel independence is our birthright,” said Dolma Choephel, 34, a social worker active with the Tibetan Youth Congress and who gathered Sunday morning at a demonstration outside the gates of the main town temple. “We understand the limitations of the Dalai Lama’s approach. What we got after six rounds of talks  this violence?” She was referring to the six negotiating sessions between the Dalai Lama and Chinese authorities since 2002.

Image A Buddhist nun at the site of Tibetan solidarity protests and prayer vigils in Kathmandu, Nepal, on Sunday. Credit... Brian Sokol for The New York Times

Just behind where Ms. Choephel stood, Buddhist monks began a hunger strike. Protesters laid down Chinese flags on the road, inviting cars and pedestrians to trample on them. Later, thousands streamed down the hill, to Dharamsala town, the largest Tibetan settlement in India. Many of them had painted their faces with the colors of the Tibetan flag. “Long live the Dalai Lama,” they chanted, which made it plain that despite their far more radical calls, they remained loyal to his spiritual leadership.

Late Sunday evening, candles were lit on window sills and balconies across these hills. Tibetan-owned shops were closed in solidarity with the demonstrations across the border.

The Indian authorities, meanwhile, found themselves in an uncomfortable diplomatic spot. The Indian police earlier last week had arrested a group of demonstrators who vowed to walk roughly 900 miles from here to Lhasa, but allowed a second group to set off Saturday morning unimpeded.