Members of the French military confronted the suspect between 8:20 p.m. and 9 p.m., using their weapons twice in an attempt to intercept him, Castaner said.
He is "known for a number of criminal offences (.) but has never been linked to terrorist offences", French deputy interior minister Laurent Nunez told France Inter radio on Wednesday.
He also said police found a grenade, a rifle and four knives during a search on Tuesday morning of Chekatt's house in an investigation over an attempted murder.
The suspected gunman has been sentenced 27 times in France, Germany and Switzerland, mostly for violence and robbery, prosecutor Remy Heitz said at a press conference.
The suspect was shot and injured by soldiers guarding the Christmas market but he escaped in a taxi, BFM TV said. "I can not say anything more, because, as you understand, searches are still underway", Nunez told the France Inter radio station.
The suspect has been identified, and police are looking for him, according to the local prefecture. He was last released from French prison in 2015, but German authorities say he was then arrested and imprisoned for theft across the border before being deported to France in 2017.
The Christmas market will be closed Wednesday and the flags will be at half-staff, Strasbourg Mayor Roland Ries said early Wednesday on his Twitter account.
He said that three people were killed and 13 injured, eight of them seriously. Four people have been detained on suspicion of having links to the suspect, who is on the run.
Amri, like Cherif C., was known as a small-time criminal before the attack and was also known to have travelled in radical Islamic extremist circles. "They, too, feared being publicly named because the gunman is still being hunted by police".
"President Emmanuel Macron, who attended a Interdepartmental Crisis Centre meeting, left without speaking to reporters but later tweeted the "solidarity of the entire nation" is with Strasbourg, the victims and their families".
Heitz said the man attacked his victims with a handgun and a knife.
The 29-year-old man sought by police over a shooting in Strasbourg lived in a small apartment in a ramshackle housing bloc and has convictions in France and several European countries after a life of crime, officials say.
"I heard over six shots and at that stage, there was chaos, confusion, everyone was running - there was pandemonium".
Other soldiers yelled for people to stay indoors and shouted 'Go home!
"From my hotel window I saw passersby dragging someone who was injured and onlookers panicking", he tweeted.
"I saw a lot of people running, scared, crying kids and all".
France remains on high alert following a series of Islamic State inspired attacks in 2015 and 2016, which killed more than 200 people.
European Parliament spokesman Jaume Duch said that "the European Parliament has been closed and no one can leave until further notice". "I am Strasbourg", in Strasbourg, eastern France, Dec. 12, 2018.
"I heard like 2 or 3 gunshots at first, which I thought were just firecrackers", Maurice said.
The Algerian and French-Algerian suspects - including an alleged associate of al-Qaida leader Osama bin Laden - went on trial in October on charges they were involved in the foiled plot for the attack.