"But we found no evidence and warning signs of a possible radicalization" Mr. Molins told the press.
"We are part of France, we are French ... so we have to, during very hard times like these, we have to be there", he said.
A police union official said the attacker had killed one person with a bullet in the head in Carcassonne before the hostage-taking.
Arnaud Beltrame, shown here in 2013, has been hailed a hero after swapping himself with a hostage in a French siege to help end a gunman's rampage (AAP).
That assault marked the first of several big Islamist attacks in France since 2015, including the massacre at the satirical newspaper Charlie Hebdo, the November 2015 attacks that killed 130 in Paris, and the 2016 Bastille Day truck attack in Nice. Another unnamed individual was arrested in connection with the shootings. Authorities said that 15 others were injured in the attack.
The 44-year-old's death takes the number killed to four. Most of the people in the supermarket escaped after hiding in a cold storage room and then fleeing through an emergency exit.
It was reported that Beltrame was among the first officers to respond to the incident and that after agreeing to the hostage swap he left his mobile phone open so that officers outside would be able to hear what was happening inside the supermarket. When police heard gunshots, however, a tactical team stormed the supermarket.
UK PM Theresa May said the "sacrifice and courage" of the police officer would not be forgotten.
Lakdim, who was armed with a gun, knife and homemade explosive devices according to a security source, was shot dead as police moved in to end his siege of the Super U supermarket where he had holed up after a shooting spree in Carcassonne. Lakdim was shot dead by police at the scene.
"He was yelling threats at people, "Everybody on the ground", Mr Guibbert said. He killed a customer and a store worker and took others as hostages. He was very aware of what he was doing. However, not only the French but the whole world need more officers like Arnaud Beltrame. One officer was shot in the shoulder but not fatally. "We're thinking any of us could have been in this shop", said one woman.
By poignant coincidence, Lt-Col Beltrame - who was married with no children - had simulated a terrorist attack at a supermarket in December in a training exercise, in his role as deputy chief of the gendarmerie in the local Aude region.
Conservative lawmaker Geoffroy Didier criticised what he called Macron's "naivety", saying the worst jihadist attack of his presidency could have been avoided. He was later chosen to join the gendarmerie's elite GSIGN in 2003, and he was deployed to Iraq in 2005.
He had previously been decorated for his bravery during operations in Iraq and spent four years in the early 2000s in France's Republican Guard, protecting the Elysee Palace in Paris.
Cedric Beltrame, the officer's brother, told RTL radio Saturday that his brother died "a hero".