The Munich-based World Uyghur Congress and Radio Free Asia, which is funded by the US government, said that police raided a house where an extended family was gathering.
Xinjiang, in China's far west, is home to the mainly Muslim Uighur minority and Chinese authorities say that "terrorists" were responsible for the incident.
But World Uighur Congress spokesman Alim Seytoff, citing information from two residents of Saybagh village, where the clash took place, said, "It was a massacre of a family who had gathered to prepare for the upcoming wedding of one of their children."
The dead included two police officers, with the other 14 all Uighurs.
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Xinjiang has for years seen spasms of violence that Beijing attributes to terrorism and separatism but rights groups say is triggered by cultural oppression, intrusive security measures and a wave of immigration by China's Han majority.
The violence peaked in 2009, when around 200 people died and more than 1,600 were injured in riots in the regional capital Urumqi.