China's official Xinhua news agency, quoting a local government spokesman, said the shootings occurred late Wednesday after a group of "violent terrorists" kidnapped two people in remote in Hotan prefecture. Xinhua said police opened fire after the kidnappers resisted arrest, resulting in the deaths of seven of them, while four others were wounded and arrested.
One police officer was killed and another wounded in the rescue attempt the report said. The two hostages were freed.
Investigators gave no other details but Xinhua said there was speculation the kidnapping was linked to an escalation of religious extremism in the Uighur-dominated far western region. The region borders Pakistan and is close to several central and west Asian countries.
The Muslim Uighurs are members of China's Turkic-speaking minority, who resent being ruled by ethnic Han Chinese.
Xinhua said in another incident earlier this month in Pishan, alleged extremists kidnapped and killed a Uygur man for drinking alcohol, which is prohibited by Muslims.