The video, dated August 1, follows the posting of a similar video in July, in which a group calling itself the Turkistan Islamic Party (TIP) claimed responsibility for bus bombings in Shanghai and Kunming, capital of the southwestern province of Yunnan.
However, Chinese officials dismissed those claims.
The comments on the online video were in the Turkic language of the Uighurs, a predominantly Muslim people in western China.
In the new video, the speaker "describes the barbarism exhibited by China towards Muslims and East Turkistan, justifying the jihad that is declared against the communist regime", SITE said.
He called on Muslims to offer support financially, physically, spiritually and verbally, according to the US-based group.
"China ... rejects Islam and forces Muslims into atheism by capturing and killing Islamic teachers and destroying Islamic schools," he said, according to SITE.
The Washington-based group said that in the earlier video TIP had threatened attacks on the Beijing games and urged Muslims to stay away.
The global intelligence analyst group Stratfor said that the Turkistan Islamic Party is another name used by the East Turkistan Islamic Movement (ETIM), an ethnic Uighur group seeking to create an independent state in western Xinjiang province.
At least 16 police officers were killed in an attack in the city of Kashgar in Xinjiang on Monday.
More than 100,000 soldier have been deployed to provide security in the capital Beijing and other cities hosting Olympic events.