The violence occurred Monday in Sichuan province's Aba prefecture, which has emerged as a center of political activism and the site of dozens of self-immolations in the past few years. The area, home to the influential Kirti Monastery, has been flooded with security forces, but they have been unable to stop the immolation protests.
Radio Free Asia said in an emailed statement that a Kirti monk named Lungtok and another man, identified as Tashi, set themselves alight Monday evening. Free Tibet, a London-based Tibetan rights group, said the two men torched themselves inside a prayer-wheel hut near the monastery before stepping out and walking toward the town's main street.
Free Tibet said police put out the flames on both men before taking them away. It said Lungtok was reported to have died and that Tashi was last seen being taken away from the county hospital with severe injuries.
The Radio Free Asia report said a large number of police tried to clear the immolation site and ended up clashing with Tibetans. It said one man was beaten to death, but gave no other details.
Free Tibet did not confirm the death but—citing an eyewitness—said one person was dragged away with a severe head injury.
The group said the police used metal batons spiked with nails to beat demonstrators.
It also said a protest broke out Tuesday in Tongren, a monastery town in neighboring Qinghai province, but did not provide details.
A woman who answered the telephone at the Aba police department said there had been no immolations or confrontations between police and Tibetan locals. "Nothing like that has happened," said the woman, who like many bureaucrats in China refused to give her name. The phone of the local Communist Party Propaganda Office rang unanswered.
A man who answered the phone at the Kirti monastery management committee office hung up when asked to comment.
Nearly 50 Tibetans have set themselves on fire in China since 2009, with many shouting anti-government slogans and calling for the return of their exiled spiritual leader, the Dalai Lama. At least 17 were monks or former monks from Kirti, according to an earlier tally from the International Campaign for Tibet.
Monday's clash with police marked the worst flaring of violence in Sichuan since a series of protests in January that Tibetan activist groups say left six Tibetans dead. The Chinese government said at the time that two rioters were killed.
The unrest comes as China enters a sensitive period, with the top leaders of the ruling Communist Party set to change by the end of this year.
China says Tibet has always been part of its territory, but many Tibetans say the Himalayan region was virtually independent for centuries until Chinese troops invaded in the 1950s.
Beijing blames the Dalai Lama for fanning anti-government sentiment and routinely purges monasteries and nunneries, where support for the Dalai Lama and Tibetan independence runs high. The Dalai Lama has not made any public statement supporting or denouncing the acts of self-immolation.
Associated Press researcher Flora Ji contributed to this report.