The Paris prosecutor’s office identified the man as Abdel-Malik Nabil Petitjean, 19. Mr. Petitjean had been on the radar of the police since June 29 for having tried to enter Syria from Turkey, and a foreign intelligence agency sent his picture to French intelligence on July 22 — four days before the attack — but without a name or description, the prosecutor’s office said.
Mr. Petitjean was born in St.-Dié-des-Vosges, in Lorraine in northeastern France, but grew up in Aix-les-Bains, in the southeast. He attended a high school there, the Lycée Marlioz, and his father lives in Montluçon, a town in central France, north of Clermont-Ferrand.
Interviewed by French reporters Wednesday night, Mr. Petitjean’s mother expressed astonishment.
She said he had last spoken to her early this week. She said: “He said, ‘Don’t worry, gets some sleep, everything is O.K.’ He had a soft voice. He sounded well. It wasn’t worrisome. He has friends, like everyone else. I have friends all over France.”
The mother told reporters, “Daesh is not part of his language,” using an Arabic term for the Islamic State, and said of her son, “He is not an introvert; he has no psychological issues.”
She said that her son had been visiting a cousin in northeastern France and that she had no idea how he had ended up in St.-Étienne-du-Rouvray, the town in Normandy where the attack occurred, although he appeared to have relatives in Normandy.
“I was a good mother,” she told reporters. “I was always there for my children, maybe even too much. Malik doesn’t have psychological problems. He’s like all 19-year-olds with ambition, with plans. He’s smart.”
At 9:25 a.m. on Tuesday, officials say Mr. Petitjean and Adel Kermiche, also 19, burst into the church, the Église St.-Étienne, in St.-Étienne-du-Rouvray, a working-class suburb of Rouen. They killed the auxiliary priest, the Rev. Jacques Hamel, and held five other hostages — two nuns and three worshipers. One of the nuns escaped, while one of the parishioners, an 86-year-old man, was critically injured. Mr. Petitjean and Mr. Kermiche were shot dead by the police.
Mr. Kermiche had been detained for nearly 10 months after trying, twice, to enter Syria, but he was released in March over the objections of prosecutors. He was made to wear an electronic ankle bracelet, forbidden to leave his local department of Seine-Maritime, required to report to a probation officer once a week and ordered to live in his parents’ house.
The measures did not prevent the killing. It was during his judge-allotted period of free movement — 8:30 a.m. to 12:30 p.m. on weekdays — that it occurred.
The Islamic State released videos on Wednesday of the two teenagers pledging allegiance to the terrorist group before embarking on their assault.
The killing of the priest has elicited condemnation worldwide and throughout France. Pope Francis, who is on his first official visit to Poland, told reporters as he flew to Krakow from Rome that “the world is at war” but added: “I am not speaking of a war of religions. Religions don’t want war. The others want war.”