At least three explosions have been reported in China's Xinjiang province, killing two people and injuring several more, Chinese state media has said.

An explosion hit a shopping area on Sunday in Luntai county, on the northern edge of the Taklamakan desert, while two more blasts were reported in nearby towns, the Xinjiang Communist Party committee said.

"At present, all the injured have been sent to hospital for full treatment, local social order is normal, and the cases are being investigated," it said.

The blasts came as China punished 17 regional officials and police "for being accountable" for a July 28 attack that led to almost 100 deaths of police, officials and civilians, and for the subsequent killing of a pro-Beijing imam.

The government said 37 civilians were killed in the July 28 attack and 59 "terrorists" were gunned down by security forces in two towns in Shache county in Xinjiang's far south. Police arrested 215 people, Xinhua said.

The government has blamed a surge in violence over the last year in Xinjiang, home to the Muslim Uighur people, on Muslim separatists.

Exiled Uighur groups and human rights activists say the government's repressive policies in Xinjiang, including curbs on Islam, have provoked unrest, a claim Beijing denies.