French authorities have identified the suspect who is on the run following a mass shooting near a Christmas market in the city of Strasbourg.

Two people were killed, one person is brain dead and a dozen others were injured in the shooting Tuesday night, prosecutor Remy Heitz said at a news conference.

Police have deployed about 350 officers in the manhunt Wednesday for the suspect whom the prosecutor identified as Cherif C., following a common practice in France for authorities to provide only an initial for a suspect's family name. The Associated Press and Reuters have reported his last name is Chekatt.

Cherif Chekatt, the suspect in the shooting in Strasbourg, France, on Dec. 11, 2018. Police National

The 29-year-old Chekatt has a lengthy criminal record with 27 offenses and has previously served jail time in France, Germany, and Switzerland.

Chekatt was radicalized in prison and was monitored by French intelligence services since his release in late 2015 on suspicion he was a religious extremist, the AP reported, citing a French interior ministry official.

Four people close to the suspect have been detained but Chekatt has yet to be caught.

Witnesses told police the suspect yelled "Allahu Akbar" (Arabic for "God is great") as he fired into the crowd near the Christmas market shortly before 8 p.m. local time (2 p.m. ET).

Strasbourg considers itself the "capital of Christmas," with its holiday market attracting millions of tourists each year.

A police car drives in the streets of Strasbourg, eastern France, after a shooting on Dec. 11. Frederick Florin / AFP - Getty Images

French Interior Minister Christophe Castaner had said the suspect exchanged shots with police after fleeing the area of the shooting late Tuesday.

He got into a taxi and the driver later told officers he appeared to be injured, Heitz said.

Hours before the shooting Tuesday, police had searched the suspect's home in a burglary probe and in the belief that Chekatt has alleged criminal association with a terrorist group and attempted an assassination. Police uncovered weapons, including a grenade and four knives in the raid, Heitz said.

Strasbourg sits on the French border with Germany. On Wednesday, the German government stepped up border controls in response to the attack, but did not change the security threat level for the country.