The attack took place Tuesday night around 1900 GMT in the heart of the medieval city as the market was closing, leaving two dead and 13 injured.
Security forces, including the elite Raid squad, spent two hours searching in Neudorf on Thursday based on "supposition only" that Chekatt could have been hiding in a building nearby two days after the attack, a French police official said.
Mr Castaner said: "The government has chose to move the security level to "Emergency Attack" with stricter controls at the borders, and the implementation of reinforced controls on all the Christmas markets that are taking place in France to avoid the risk of copycat attacks".
The dragnet was aimed at catching the suspect "as soon as possible", no matter whether he was dead or alive, and "put an end to the manhunt", Griveaux said.
The suspected gunman grew up in the city and had a checkered past.
Chekatt's neighbors say he was "destabilized" in prison, according to AP.
Chekatt has known ties to extremist groups, officials said.
Police issued a wanted poster for Cherif Chekatt, who was on an watch list as a potential security threat.
Last Saturday almost 90,000 police were mobilised across the country for the protests, with 8,000 officers and a dozen armoured vehicles deployed in the capital where scores of stores, museums and monuments were closed.
The officers had then shot and killed him.
The death toll from Tuesday's attack rose to three while police on Thursday combed the city in the east of France for a second day and manned checkpoints on the German border in their search for Chekatt.
Chekatt has an extensive criminal background that includes 27 convictions in France, Germany and Switzerland, mostly for acts of robbery and violence.
Police distributed a photo of Chekatt, who was wounded in an exchange of fire with security forces, with the warning: "Individual unsafe, above all do not intervene".
Witnesses said that the suspect, previously identified as Cherif Chekat, was yelling "Allahu Akbar" (God is great) during the shooting rampage, Remy Heitz, the Paris prosecutor, told a press conference on Wednesday.
While some of the movement's representatives have said they are open to halting the protests to negotiate with the government, others have said its concessions are not enough, and have vowed to protest again in Paris this weekend.
France has been targeted by a series of attacks by Islamist gunmen since 2015, and the Strasbourg market was long considered a target.
Italian Interior Minister Matteo Salvini said one Italian was among the wounded, in critical condition.
The Christmas market, a hugely popular attraction in historic Strasbourg, will reopen on Friday, Castaner said.
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O2 has confirmed problems with mobile data across its network this morning (Thursday, December 6, 2018). ). This means that the number of impacted customers is, in reality, likely to be much higher than 25 million.
This is the kind of game if you score in the first minute you normally go for a different performance. The 23-year-old England left-back has started all of United's games in the Champions League this term.
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