"Today, the Annecy prosecutor's office opened a preliminary investigation into attempted murder and armed resistance," Mathis said in a televised press conference.
Mathis said that the six victims of the attack - four young children and two adults - were out of any danger.
"The psychiatrist found no obvious signs of psychiatric abnormalities, but it is too early to make a final assessment and say whether or not there is mental illness at this stage," Mathis said, adding that there were no traces of alcohol or drugs in the attacker's blood.
The assailant was found in possession of a folding knife, which he used in the attack, two Christian icons, a cross and a Swedish driver's license.
The attack took place Thursday morning in a park near Lake Annecy in the department of Haute-Savoie. The attacker was identified as a Syrian born in 1991. He requested political asylum in France in November 2022, but the request was rejected four days prior to the attack on the grounds that he had already been granted refugee status in Sweden.
According to media reports, the attacker had lived in Sweden for more than 10 years, was married, and had a three-year-old child. He has been seeking asylum in France, Italy and Switzerland in the past few years.
The mayor's office in Annecy organized an event on Sunday in support of the victims of the attack and their loved ones, according to its website. Local residents bring flowers, candles and toys to the site of the attack in the park, according to a video report on French TV.