While there were fears he may have fled into neighbouring Germany French police concentrated their searches on the Neudorf and Meinau areas, where Chekatt grew up.
The suspected Strasbourg gunman was convicted of robbery in Germany in 2016 and sentenced to two years and three months in prison for breaking into a dental practice and a pharmacy.
Interior Minister Christophe Castaner told reporters later three police officers came across a man they believed to be Chekatt and went to arrest him.
French authorities issued instructions for Chekatt to be caught "dead or alive".
A top French official told the Associated Press news agency that a man had been killed in a shootout with police during the operation to trace Chekatt, but declined to confirm his identity on Thursday.
More than 700 officers were involved in the manhunt and prosecutors have opened a terror investigation into Tuesday's attack.
The man suspected of launching a deadly shooting and stabbing rampage in the centre of Strasbourg this week was shot dead by French police on Thursday evening.
On Thursday afternoon, dozens of French police including members of the elite RAID force cordoned off an area of southern Strasbourg where the gunman was last seen.
Another unnamed neighbor said the shooting suspect was rarely home.
French soldiers, who are part of anti-terrorism patrols across the country, had shot him in the arm but he managed to escape and elude capture for 48 hours.
So far, five people have been arrested and remanded in custody in connection with the investigation, including Chekatt's parents and two of his brothers. French prosecutors said the suspect shouted the Arabic phrase "Allahu Akbar", meaning "God is greatest", at the time of the attack.
Asked if police had been told to capture the killer dead or alive, government spokesman Benjamin Griveaux earlier told France's CNews: "It doesn't matter".
But he called on the protesters to be "reasonable" after President Emmanuel Macron offered a range of financial relief last Monday, including a minimum wage boost and a tax cut for low-income pensioners.
Italian Interior Minister Matteo Salvini said one Italian was among the wounded, and was in critical condition. Police in the German town of Kehl said they had received reports of possible sightings but all were false leads.
France has been targeted by a series of attacks by gunmen since 2015, and the Strasbourg market was long considered a target.
The head of the European Commission, the EU's executive body, Jean-Claude Juncker, tweeted: "My thoughts are with the victims of the Strasbourg shooting, which I condemn with the utmost firmness". He listed violence since 2015 that killed more than 200: at the Charlie Hebdo satiric newspaper, a Kosher store, restaurants, bars and a concert hall in Paris; along the famed seaside promenade in Nice; and even inside a church in a quiet suburb of the northern city of Rouen, among others.
Their weeklong bash is said to include at least five events , and Bloomberg reported a cost estimate of $100 million. The respective families will hold several other receptions across India's financial capital in the coming days.
Millions of people have been having problems with their mobile phones this morning, after the O2 network went down. The company have so far not said anything about whether they would be giving customers compensation for the outage.
Nasa said that the air pressure sensor used to collect meteorological data recorded these air vibrations directly. Hindustan Times delivers the news across all social media platforms, on the web, and at your doorstep.
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The team that I will play tomorrow, I want to put out a team where they can cope well with that happiness with a decisive game. Mourinho claimed that his players should have treated the Palace match as "special", arguing that they failed to do so.
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Danvers is then heard asking, "What aren't you telling me?" over a shot of Jude Law's charcter, who doesn't seem too helpful. If you're a Marvel Comics reader, you're probably aware of the issues between the Krees and the Skrulls .
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