French police have identified the suspect as Strasbourg-born Cherif Chekatt, 29, who was known to intelligence services as a potential security risk.
A photo of Cherif Chekatt was distributed by French police on Wednesday.
French authorities have appealed to the public to remain vigilant as the suspect is still on the run and not to approach him, but instead call a hotline.
The poster reads: “Dangerous individual, above all do not intervene”.
Chekatt has been on the run since allegedly spraying gunfire at the city’s famous Christmas market on Tuesday, killing two and leaving one person brain-dead. A dozen others were injured.
The dead included a Thai tourist, 45-year-old Anupong Suebsamarn, according to Thai Foreign Ministry and the website of the Khao Sod newspaper. It quoted his uncle as saying he and his wife had originally planned to visit Paris, but the protests there prompted them to change plans and go to Strasbourg instead.
One Italian was reported to be among the wounded. Italian media said Antonio Megalizzi, 28, was in critical condition. Italian daily La Repubblica reported he was in Strasbourg to follow the session of the European Parliament.
French police have circulated the poster of the suspect on Twitter and provided a link to a website where individuals are able to submit information that could assist the investigation.
France has raised its three-stage threat index to the highest level and bolstered troops around France.
Interior Minister Christophe Castaner told politicians that Chekatt had run-ins with police starting at age 10 and his first conviction at age 13.
He had been convicted 27 times, mostly in France but also in Switzerland and Germany, for crimes including armed robbery. He had been flagged for “extremism” and was on a watch list, but the interior minister said: “the signs were weak.”
Hundreds of police and soldiers were combing Strasbourg in search of him, blocking bridges that cross the border into Germany.