The statement from the World Uyghur Congress, which Beijing considers a separatist group, came one day after state-run media reported Chinese authorities had named two suspects from the restive far western region of Xinjiang following the incident.
A sport utility vehicle ploughed through crowds at the capital's best-known site - where huge pro-democracy demonstrations were held in 1989 - killing five people, including three in the car and a woman tourist from the Philippines, and wounding 38.
East Turkestan is the name which the activist organisation uses to refer to Xinjiang, where Uighurs, many of whom are Muslim, make up 46 per cent of the population.
The group added that it fears the response by authorities in Beijing will "lead to further demonisation of the Uighur people and incite a fierce state crackdown" in Xinjiang.
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"The Chinese government will not hesitate to concoct a version of the incident in Beijing, so as to further impose repressive measures on the Uighur people," Kadeer said.
But Ilham Tohti, a prominent Uighur intellectual, told AFP that he feared the event "could lead local governments to increase repression and discrimination" against the minority group and that evidence that the incident was a terror attack carried out by Uighurs was lacking.
Beijing has pointed to violent incidents in Xinjiang as evidence of rising extremism among the ethnic minority, but information in the far western region is tightly controlled and Uighur organisations complain of cultural and religious repression.
One of the suspects named in Monday's reported police notice was from Lukqun, where state media said 35 people were killed in June in what Beijing called a "terrorist attack".