French police are linking the shootings of four people at a Jewish school in Toulouse to the killings of three soldiers of North African descent in two separate incidents last week.
The same gun and the same stolen scooter were used in all three attacks, sources close to the investigation say.
A teacher and three children were shot dead at the Ozar Hatorah school, and a teenage boy was seriously injured.
One of the biggest manhunts in France in recent times is now under way.
President Nicolas Sarkozy, who flew to Toulouse in the wake of the attack, described it as a "national tragedy". He said a single person had carried out all three attacks and that an "anti-Semitic motive" seemed obvious.
Guards are to be posted outside all faith-based schools, as well as all Jewish and Muslim religious buildings, he said.
Mr Sarkozy has also placed south-west France on the highest level of terrorism alert.
All schools in France will observe a minute's silence on Tuesday morning at 11:00 (10:00 GMT).
The latest shootings took place as parents were taking their children to the school on Monday morning.
Witnesses said the gunman pulled up on a black scooter and began shooting at an area which serves as the drop-off point for the school's nursery- and primary-age children.
"This man alighted from his moped and, as he was outside the school, he shot at everybody who was near him, children or adults. Children were chased right into the school," local prosecutor Michel Valet told journalists.
The scooter - a black Yamaha - was stolen in Toulouse on 6 March, five days before the first shooting. Its number plate was picked up by closed-circuit TV cameras at the school, police sources said.
The dead were Jonathan Sandler, a 30-year-old rabbi and teacher of religion originally from Jerusalem, and his two sons, aged three and six. The fourth person killed was an eight-year-old girl, daughter of the head teacher.
All the dead were dual French-Israeli nationals and will be buried in Israel, the Israeli Foreign Ministry said.
A 17-year-old boy was seriously hurt. The head of Toulouse's Jewish community told the AFP news agency the boy had undergone several operations but he was likely to recover.
Initially, the killer used a 9mm gun, but when it jammed, he switched to a .45 calibre weapon.
Police say the .45 was the same gun used to kill three soldiers in two separate shootings in Toulouse and the nearby city of Montauban last week. All three were of North African or Caribbean origin.
A paratrooper out of uniform was shot dead in a residential area of Toulouse just over a week ago, while two soldiers were killed and a third wounded as they used a cash machine in the town of Montauban, some 29 miles (46km) away, on Thursday.