France launched one of the biggest manhunts in recent country’s history after three children and one adult were shot dead at Ozar Hatorah Jewish school in Toulouse.
French police have linked the attack to two shootings last week in which three soldiers of North African descent died.
The same gun and the same scooter were used in all the attacks, but the gunman has not been identified, officials say.
French schools held a minute’s silence on Tuesday. The area is on the highest level of terrorism alert.
It is the first time in the country’s history that “scarlet alert” has been declared.
The measure enables the authorities to disrupt daily life and implement sweeping security measures, including mixed police-military patrols, powers to suspend public transport and close schools.
Guards are being posted outside all faith-based schools, as well as all Jewish and Muslim religious buildings.
About 200 investigators from Paris are pursuing two main lines of inquiry – an Islamist motive or the far right.
However, Interior Minister Claude Gueant told French radio the authorities did not know who the killer was.
“For now, we carry on working. We’re no further than that,” Claude Gueant said.
The minister said “a witness saw a small video camera around the killer’s neck” and the authorities were combing the internet for any possible footage.
Claude Gueant said this was an important clue allowing police to build a psychological profile of the killer, who he described as “clearly very cold, determined and master of his actions”.
But there was no sign police were near making an arrest.
A teacher and three children were shot dead at the Ozar Hatorah school in Toulouse, and a 17-year-old boy was seriously injured.
The shootings took place as parents were taking their children to the school on Monday.
“This man alighted from his moped and, as he was outside the school, he shot at everybody who was near him, children or adults,” local prosecutor Michel Valet told journalists.
The scooter – a black Yamaha – was stolen in Toulouse 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 4 and 5.
The fourth person killed was 7-year-old girl Myriam Monsonego, daughter of the head teacher. She died in her father’s arms.
All the dead were dual French-Israeli nationals and will be buried in Israel, the Israeli foreign ministry said.
The 17-year-old boy was seriously hurt. Initially, the killer used a 9 mm gun, but when it jammed, he switched to a .45 calibre pistol.
Police say the .45 was the same gun used to kill three soldiers in two separate shootings in Toulouse and nearby Montauban last week. All three were of North African or Caribbean origin.
The mother of a girl at the Toulouse school said she was angry with the authorities who she said had not taken last week’s incidents seriously enough and had “lost time to look for this man”.
Since the early 1980s have not been lethal attacks like this in France on Jewish targets. And even then, children were never the primary victims.
All the candidates in the French presidential election have suspended campaigning.
President Nicolas Sarkozy said his campaign would remain suspended until Wednesday at the earliest, when he is due to attend the soldiers’ funerals.
As well as Nicolas Sarkozy, opposition Socialist candidate Francois Hollande visited Toulouse to offer his condolences. Far-right candidate Marine Le Pen called on the authorities to do everything to prevent another such attack.
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