“Xinjiang is a region where we have documented severe human rights abuses both by the police and ordinary officials,” said Maya Wang, a researcher for Human Rights Watch. “Anything that would involve training government officials involved in this repression would be contributing to human rights abuses.”

United States officials have taken notice. Lawmakers have introduced bipartisan bills that urge the Trump administration to punish Chinese officials and to prevent sales of some American equipment to some Chinese state agencies. Officials at the White House and in the State and Treasury Departments have been discussing whether to impose economic sanctions on Chinese officials who oversee the system of repression in Xinjiang.

Mr. Prince made a name for himself as the founder of Blackwater, a private military contractor that did business in Iraq. After Blackwater employees were held responsible for civilian deaths in Baghdad, Mr. Prince sold the company and set up FSG, turning his sights to the growing demand from Chinese companies moving into countries and regions with ethnic strife.

FSG, which is listed in Hong Kong, has unabashedly courted Chinese officialdom. Citic Group, one of China’s biggest state-owned conglomerates, owns a quarter of FSG’s stock. A security and logistics company, FSG has tied itself to China’s Belt and Road Initiative, a major campaign by President Xi Jinping to develop geopolitical ties by building bridges, trains and ports through Asia. China considers Xinjiang, which borders Kazakhstan and several other Central Asian countries, a gateway to a strategically important region.

Tumxuk lies between Kashgar and Aksu, larger settlements that have been a focus of the Chinese government’s drive to stifle antigovernment sentiment. The city comes under the Xinjiang Production and Construction Corps, an organization run along military lines and founded in the 1950s to bring security, development and Han Chinese settlers — members of China’s largest ethnic group — to the region. Even now, the corps acts as a kind of parallel administration in Xinjiang, holding vast areas of land and operating its own schools, courts and other institutions.

But Tumxuk has also been drawn into the regionwide drive to transform Uighur society through indoctrination camps.

The government says the camps wean Uighurs and other Muslim minorities from religious extremism, while teaching them Chinese language and job skills. But former inmates have described harsh, even brutal treatment, and United Nations human rights committees and experts have condemned the camps for holding people in the camps without legal appeal.