Mr. Molins said that Mr. Lakdim had been flagged by French intelligence services in 2014 “because of his radicalization and of his ties to the Salafist movement,” and that he had been under surveillance in 2016 and 2017.
But Mr. Molins said the surveillance had not uncovered “any precursory sign that could have foretold a terrorist act.” He denied reports that Mr. Lakdim had tried to travel to Syria.
The Islamic State claimed responsibility for the attack, describing the assailant as a “soldier of the Islamic State” and the attack as a response to its call to target “coalition countries,” meaning countries that have fought against the group.
The wording suggested that the attacker was inspired by the Islamic State, rather than directed by it. The group has made clear that no direct link is needed to carry out attacks in its name, although some of the deadliest assaults in Europe have been perpetrated by sympathizers guided by Islamic State operatives online.
Mr. Molins said that Mr. Lakdim first hijacked a car in Carcassonne on Friday morning, killing the passenger and wounding the driver. He then targeted a group of police officers returning to their barracks after a jog, shooting at them and wounding one.
Finally, Mr. Lakdim drove to the market, the Super U in nearby Trèbes, where he killed two more people and took several hostages. Gérard Collomb, the French interior minister, said a 45-year-old police officer voluntarily traded places with them.
The officer, a lieutenant colonel with France’s gendarmerie identified by French officials as Arnaud Beltrame, left his phone on a table with an open line, Mr. Collomb said, enabling the police outside to listen in.
After more gunshots were heard, the police stormed the store and killed Mr. Lakdim. Colonel Beltrame was “seriously wounded” in the exchange of gunfire, Mr. Collomb said, praising him for an “act of heroism.”
Mr. Macron, speaking from the Interior Ministry in Paris after returning from a European Union summit meeting in Brussels, said Colonel Beltrame had “saved lives” and honored his profession and his country.
About 50 people were in the market in Trèbes at the time of the attack, Mr. Molins said, although he could not specify how many were taken hostage. The gunman shouted “God is great” in Arabic as he entered, witnesses said.
“Saying that he was ready to die for Syria, he called for the liberation of his brothers, before shooting at a client and a store employee, who both died on the spot,” said Mr. Molins, speaking at a news conference in Carcassonne.
Several French news reports said that Mr. Lakdim had demanded the release of Salah Abdeslam — the only surviving member of the Islamic State group that killed 130 people in and around Paris in a series of coordinated attacks in November 2015 — from detention in France.
Mr. Collomb did not directly confirm those reports, saying only that he had called for the “liberation of prisoners” and that it was unclear how he had chosen his targets on Friday.
Christian Guibbert, a retired police officer, told reporters that he was shopping in the market with his wife and his sister-in-law when he heard gunshots and saw a “very agitated” man with a handgun and a knife, yelling and shooting into the ceiling.
“He was yelling threats at people, ‘Everybody on the ground,’” Mr. Guibbert said.
He said he hid his wife, his sister-in-law and other customers in a meat locker and then called the police. “That’s when he saw me and ran after me,” Mr. Guibbert said, describing how he escaped through an emergency exit.
France continues to be on high alert after deadly terrorist attacks struck the country in 2015 and 2016, mainly in Paris and Nice. Although there have not been any large attacks since the one in Nice in July 2016, there have been several smaller-scale assaults by lone individuals, and the French authorities regularly announce that new plots have been thwarted.
One of the first major cases of homegrown terrorism in France occurred in 2012, in the area around Toulouse, where Mohammed Merah killed three French soldiers and four others, including three children, at a Jewish school. He had traveled to Afghanistan and Pakistan to seek training as a fighter.
The deadly attack in Trèbes is the first since Mr. Macron’s government lifted the state of emergency that had been in place since the November 2015 attacks and Parliament passed a counterterrorism law that made permanent some of the emergency measures.
France also recently unveiled plans to toughen its stance on combating extremism in prisons and schools.
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