The ICT, a Tibetan rights group, said government work teams had been sent to Biru, known as Driru in Tibetan, ahead of the national holiday to compel local Tibetan residents to fly the flag as part of an intensified effort to enforce loyalty to the Communist Party.
In Sunday's unrest, protesters were calling for the release of a local resident, Dorje Draktsel, who was detained last week after participating in demonstrations against the flag order, Radio Free Asia said.
The self-proclaimed Tibetan government-in-exile based in India said it had received reports of the firing in Driru but had few details. Spokesman Tashi Phuntsok said by phone that they had heard some protesters were injured but did not know how many.
Free Tibet said it had the identities of five of the injured Tibetans. It named two victims who it said were taken to a Lhasa hospital in critical condition.
China has claimed Tibet as part of its territory for centuries, while Tibetans say they were largely independent prior to the occupation by Communist troops in 1950.
Many Tibetans say Beijing's economic policies in the Himalayan region have mainly benefited Chinese migrants and resent the government's strict limits on Buddhism and Tibetan culture. China says it has made vast investments to boost the region's economy and improve the quality of life for Tibetans.
Meanwhile, in the northwestern Muslim region of Xinjiang, an official Chinese newspaper said authorities have detained more than 100 people from late June to the end of August for the spread of "religious extremism."
The detentions, reported by the Xinjiang Daily, are the latest in an official campaign in Xinjiang to police the spread of ideas critical of Chinese government rule. The government is also pouring troops into the restive region.
Germany-based Uighur activist Dilshat Rexit said Chinese authorities were using such charges as an excuse to crack down on Uighurs who go on the Internet to express their unhappiness about government repression.
Xinjiang has periodic outbreaks of anti-government and anti-Chinese violence, some of it inspired by resentment over economic marginalization by Chinese ethnic Han migrants who have flooded into the region in recent decades, along with restrictions on Uighur social and cultural life.
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Associated Press writer Ashwini Bhatia in Dharamsala, India, contributed to this report.