The vehicle crashed into a crowd and burst into flames, killing five people.
Police subsequently issued a notice to hotels in Beijing seeking information about two people from Xinjiang province, Chinese media said.
The note also described a vehicle and four number plates from Xinjiang, the scene of sporadic violent incidents.
State-run Xinhua news agency said of the five people who died on Monday, three people died inside the car and two tourists were killed. Another 38 people were injured.
Police shut down the scene of the incident – at the north end of the square at an entrance to the Forbidden City – shortly after it occurred, temporarily closing a subway station and a road.
There has been no official statement on the cause of the incident.
“A major case has taken place on Monday,” the police notice said, without specifying what. It named two residents from Xinjiang’s Pishan and Shanshan counties as suspects.
The notice, unconfirmed images of which have been widely circulated on Chinese social media, also asked hotels to look out for “suspicious guests” and vehicles.
China’s state-controlled Global Times said it had confirmation from the Beijing police that the notice was genuine, although police did not comment on the “major case” itself.
Zhao Fuzhou, a security official at Beijing’s Xinjiang Dasha hotel, said that police had circulated a notice to hotels searching for information about two suspects with Uighur names, AP news agency reported.
Xinjiang is home to the minority Muslim Uighur group, some of whom complain of cultural and religious repression under Beijing’s rule. There have been sporadic outbreaks of violence in Xinjiang, including both Pishan and Shanshan counties.
China says it grants the Uighurs wide-ranging freedoms.
On Monday a Chinese Foreign Ministry spokeswoman said she did not know “specifics” about the incident. The country’s main state-run news agency, Xinhua, on Monday offered no reason for the incident but said police were investigating.
Tiananmen Square is a highly sensitive site due to its link to China’s 1989 pro-democracy protests, which were ended by a military crackdown.
The square is generally kept under very tight security both because of its proximity to key political institutions and so that is does not serve as a hub for protesters and petitioners, although incidents have nonetheless occurred there before.
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