Chinese state-run media has defended the government's treatment of a revered Tibetan monk who died in prison last week, after rights groups and his family slammed the handling of his death.

Tenzin Delek Rinpoche, 65, was 13 years into a life sentence for terrorism and separatism, imposed following a trial which observers said was deeply flawed, when authorities announced news of his death at the weekend.

Rights groups said the circumstances of his death were unclear and the family said Delek was cremated against their wishes.

But Xinhua news agency said authorities had been quick to treat Delek after finding him "suffering respiratory failure", though he subsequently died of a heart attack.

"The monk's right to health care has been guaranteed since his imprisonment," Xinhua said, adding that Delek had sometimes refused treatment for an unspecified "disease".

Delek was cremated on Thursday before Tibetan burial rights could be carried out, according to Students for a Free Tibet.

And on Friday Delek's sister and her daughter were taken away by police in the southwestern city of Chengdu, SFT said, citing Geshe Nyima, Delek's student and cousin.

Several protests in Delek's home town and in Chengdu, where he was jailed, have taken place since his death was announced, according to the US-based International Campaign for Tibet and other rights groups.

Police opened fire when around 1,000 people gathered near government offices in Nyagchuka county to protest at the death, injuring about 20 people, the British-based Free Tibet group said.

Access to Tibetan regions is tightly controlled by the Chinese government and local media are barred from investigating issues the government deems sensitive.

China, which has ruled Tibet since the 1950s, has been accused of trying to eradicate its Buddhist-based culture through political and religious repression and large-scale immigration by Han Chinese, the country's ethnic majority.

China says that Tibetans enjoy extensive freedoms and that it has brought economic growth to the region.

Tibetan spiritual leader the Dalai Lama fled Tibet after an abortive uprising in 1959 and established his government-in-exile in Dharamsala in India.(AFP)