The self-proclaimed Tibetan government in exile has called on Tibetans to stop setting fire to themselves to protest against what activists say is Beijing's heavy-handed rule in the region.

"We understand what is driving them to do it but we appeal to Tibetans not to go for these extreme acts," a spokesman told the Guardian.

The call comes after a Tibetan farmer set himself ablaze in front of a market in remote north-west China on Tuesday. It was the second such death in 48 hours. Both protests occurred close to the Labrang monastery in Gansu province, the site of numerous protests after deadly ethnic riots in 2008.

The two deaths bring the total self-immolations to 58 since March 2011 with eight in the past month, campaigners say. Many of those setting themselves alight have called for the return of the Tibetans' spiritual leader, the Dalai Lama, as they have died. The Chinese government has confirmed some, but not all, of the self-immolations. "There is no basic freedom in Tibet. That is why people commit these extreme actions. We are very, very concerned but they are the ones inside Tibet suffering. They are the ones to decide," the spokesman for the Tibetan government in exile said.

The Washington-based International Campaign for Tibet named the most recent man to die as Dorje Rinchen, a farmer in his late 50s, who it said set himself on fire on the main street in Xiahe township and died later. The group quoted a Tibetan from Xiahe who currently lives in exile as saying that Dorje had asked young Tibetans not to follow his example.

Despite such appeals, support in Dharamsala in India – where the Dalai Lama is based – appears strong for the dramatic protests, however.

"It's a reminder of our situation, and a wake-up call for the rest of us, especially the younger generations," said Nyima Dorjee, a 23-year-old Tibetan-born cook. "Freedom never comes for free. We can't just sit doing nothing. One has to hit a stone against the wall to make a sound."

In an attempt to stop such protests, police in Gansu have offered rewards of $7,700 for information about planned self-immolations.

The local police force said on Sunday that the immolations had "seriously impacted social stability and harmony as well as people's ability to live and work." Informers will receive 50,000 yuan ($7,700) for tipping police off about immolation plans and up to 200,000 yuan for providing information on the "black hands" who help organise such protests, the police said.

"Self-immolation is an extreme suicidal behaviour that goes against humanity, society and the law and deprives people of their right to life," it said. "The instances of self-immolation that have occurred recently in our prefecture are part of a political conspiracy by the Dalai clique that means to split China and undermine national unity."

The Dalai Lama, who fled Tibet to India in 1959 amid a failed uprising against Chinese rule and has been based in Dharamsala ever since, has neither condemned nor encouraged the immolations, simply saying that it is "difficult to judge if these methods are right or wrong".

Suicide is forbidden in Buddhism, but could be justified if the motives are pure, such as a genuine desire to help others through self-sacrifice.

Posters showing the faces of the dead – dubbed "martyrs" – now line streets in Dharamsala and there are frequent memorial events, such as candle-lit vigils. A drama staged this week at the main school for Tibetan refugees in the town depicted a self-immolation, locals said.

"I feel sad, like the rest of the Tibetans. I am old and I have seen a lot [of bad things] throughout my life," said one resident, Yedrong, 68. "But now seeing those brave souls I have hope." Chinese authorities routinely deny Tibetan claims of repression and have accused supporters of the Dalai Lama of encouraging the self-immolations.

China's foreign ministry on Wednesday repeated its claim that supporters of the Dalai Lama have been inciting the deadly protests "to achieve their separatist goal".

China says Tibet has always been part of its territory. Tibetans say the Himalayan region was virtually independent for centuries.

Most of the recent self-immolations have been in a broad swath of the east of what was historically considered Tibet but which is now inside the Chinese provinces of Gansu, Qinghai and Sichuan.

Some experts say this is because issues of cultural identity in these more mixed regions are problematic for young Tibetans living there compared to the Tibetan heartland. Others say it is simply because the authorities have less control, with fewer restrictions on the internet, for example.

The tactic is non-violent and thus respects the spirit of the Dalai Lama's "middle way" strategy despite increasing frustration inside Tibet with the lack of progress the approach has brought, one Dharamsala-based analyst said.