The protester apparently had doused himself with something highly flammable and was engulfed in flames when he ran past the podium where speakers were criticizing China and the visit by President Hu Jintao.
Fellow activists beat out the flames with Tibetan flags and poured water onto him. He was on fire perhaps less than two minutes, but some of his clothing disintegrated and his skin was mottled with black, burned patches by the time he was driven to a hospital.
The man, identified as Jampa Yeshi, sustained burns on 85 percent of his body and his condition was critical, a senior police officer said. He spoke on condition of anonymity because he was not authorized to speak to the media.
Protesters initially prevented police from taking him to the hospital, but officers eventually forcibly took him away.
Yeshi, 27, escaped from Tibet in 2006 and had been living in New Delhi for the past two years, activists said.
Hu is expected to arrive in India on Tuesday for a five-nation economic summit.
While activists had been whispering on Monday morning that something dramatic was expected at the protest, organizers insisted they were not behind the self-immolation.
"We have no idea how this happened, but we appreciate the courage," said Tenzing Norsang, an official with the Tibetan Youth Congress. He called on the international community to talk about Tibet at the summit.
"If you care about peace you should raise the issue of Tibet," he said. "Hu Jintao is responsible for what is happening there."
The New Delhi protest comes amid a series of self-immolations inside Tibet. About 30 people - many of them monks or nuns, and often in their teens or early 20s - have lit themselves on fire over the past year, calling for the return to Tibet of the Dalai Lama and to protest Chinese rule over their homeland. The Dalai Lama, who fled Tibet amid a failed 1959 uprising against Chinese rule, has blamed China's "ruthless policy" for the self-immolations. China accuses the Dalai Lama of stirring up trouble.
At the site of the protest, a large poster of Hu - with a bloody palm print over his face - said: "Hu Jin Tao is unwelcome" at the summit.
More than 600 demonstrators marched across New Delhi to a central plaza near the Indian Parliament to protest Hu's visit. Some carried posters saying "Tibet is burning" or "Tibet is not part of China."
China says Tibet has always been part of its territory. Tibetans say the Himalayan region was virtually independent for centuries.
Monday's was the second self-immolation in India in recent months. Last year, a young Tibetan exile set himself on fire outside the Chinese Embassy. That man suffered minor burns.
"This is what China faces unless they give freedom to Tibet," said Tenzin Dorjee, a young onlooker.
Hu will be attending a summit this week of the leaders of Brazil, Russia, India, China and South Africa, who form a grouping known as BRICS.
Police in New Delhi are bracing for protests by the tens of thousands of Tibetan exiles who live in India. Security around the summit location has been tightened, and roads leading to the hotel will be closed to the public a day ahead of the meeting.
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