TOULOUSE, France — A day after an attack outside a Jewish school here killed a rabbi and three young children, the French authorities offered fresh details on Tuesday of an assault that has stunned the nation and terrorized the city, saying the lone gunman seemed to be filming his actions as he coolly shot his victims to death.

Claude Guéant, the interior minister, told a French radio station that surveillance footage from the school’s security cameras showed what appeared to be a video camera strapped to the gunman’s chest — adding a lurid detail to the most deadly attack against Jews in France in 30 years.

With the nation’s terrorism alert at its highest level — “scarlet” — the French authorities pursued a broad and high-profile search on Tuesday for the assailant, but Mr. Guéant said little was known about him.

The attack has been linked to two earlier shootings of French paratroopers, with the police saying that the same gun, a .45-caliber automatic pistol, was used in all three assaults. The authorities have also said that the methods were the same — a man on a powerful motorbike, also the same in each instance, who killed and then fled.