attack in which an SUV with a family of three ploughed into a group of people at the Square on Monday noon in a planned act of terrorism.
Five people including the three in the vehicle were killed and at least 40 others were injured in the crash and subsequent blaze which the occupants had triggered.
Beijing police said the three in the vehicle were a man with an ethnic Uyghur name, his wife and his mother. Police arrested five people on suspicion of conspiracy.
Knives, iron rods, petrol and a flag imprinted with religious slogans were found in the vehicle, police said.
The group is yet to claim responsibility for the attack.
Meng, chief of the commission for political and legal affairs of the ruling Communist Party of China (CPC), named ETIM in an interview with Hong Kong-based Phoenix Television.
At the time of the interview, Meng was in Tashkent the capital of Uzbekistan attending a regional security summit and seeking co-operation on counter-terrorism.
"The violent terrorist incident that happened in Beijing is an organised and plotted act. Behind the instigation is the terrorist group East Turkestan Islamic Movement entrenched in central and west Asian regions," Meng said in the video footage aired by Phoenix.
Meng gave no further detail.
China has frequently blamed the group for inciting violence in the country's far west, Xinjiang Uyghur Autonomous Region (XUAR), saying it wants to create an independent state of East Turkestan.
The government says the group and its sympathisers in Xinjiang, China's largest province bordering a number of Central Asian states besides Pakistan, Afghanistan and India, were responsible for carrying out "terrorist acts" like attacking police stations and government symbols like municipality and county offices.
In May this year, a joint statement issued in Islamabad during Premier Li Keqiang's visit, said China and Pakistan regard the "terrorist ETIM group as a common threat, and stand united in upholding China's sovereignty and territorial integrity".
Scholars and rights groups have dismissed the blame, saying the ETIM threat is vastly exaggerated by the Chinese government and the group – if it does exist in an oragnised form – does not have the capability to carry out terrorist attacks.
Rights groups say China uses the ETIM threat as an excuse to impose religious and cultural restrictions on the Uyghurs. And decades of suppression by Beijing, in turn, has fuelled homegrown extremism in the region.
Activists add that Uyghurs have received little benefit from the exploitation of Xinjiang's natural resources. The 8 million Uyghurs now make up about 43% of the population in a region where they used to dominate because of state-supported migration by the majority Han community.