Meng Jianzhu, chief of the Commission for Political and Legal Affairs of the ruling Communist Party, blamed the group, saying: "The violent terrorist incident that happened in Beijing is an organised and plotted act."
An SUV ploughed through bystanders, crashed and burst into flames near the Tiananmen Gate on Monday, killing three in the car and two tourists, including a Filipino woman, and injuring dozens.
Beijing police said the perpetrators were a man with an ethnic Uighur name, his wife and his mother. Police also have arrested five people - identified with typically Uighur names - on suspicion of conspiring in the attack and called it a planned terror strike, the city's first in recent history.
Uighurs are an ethnic minority living mainly in China's north-west.