TOULOUSE, France — The French authorities were searching on Monday for a man suspected in a string of methodical killings that have terrorized this city and the surrounding area in southwestern France, after an attack outside a Jewish school on Monday morning that killed four people, including three young children.

It was the third murderous attack on unarmed people in the region in little over a week, and the most deadly attack against Jews in France since a 1982 assault on a Paris kosher restaurant. The police said that the same gun, a .45-caliber automatic pistol, was used in all three shootings, the one Monday and two earlier attacks on French paratroopers, and that the modus operandi was the same — a man on a powerful motorbike, also the same in each instance, who shot and then fled.

The local prosecutor, Michel Valet, said that a religious instructor, his two children and another child, the daughter of the school’s director, were killed in Monday’s attack and that a 17-year-old boy was seriously wounded. The killer “shot at everything he could see, children and adults, and some children were chased into the school,” Mr. Valet said.

The suspect pursued his last victim, an 8-year-old girl, into the concrete courtyard, seizing and stopping her by her hair, said Nicole Yardeni, who leads the regional branch of the Crif, France’s most prominent Jewish association, and who viewed video surveillance footage of the killing.