(Reuters) - A gunman shot dead three children and a rabbi at a Jewish school in Toulouse on Monday, days after killing three soldiers nearby, prompting French President Nicolas Sarkozy to put the region on its highest terrorism alert.

With the attacker, who escaped on a motorbike, still on the loose, police stepped up a manhunt in the city of a million people in southwestern France. Sarkozy said the killings and those of the soldiers, one of Caribbean and two of Muslim origin, in two attacks last week, appeared to be motivated by racism.

Mourners gathered for an overnight vigil at the Ozar Hatorah school in a leafy residential neighborhood in Toulouse, where the gunman went on the rampage on Monday morning, killing a 30-year old rabbi Jonathan Sandler, his children aged four and five, and another child, the daughter of the school´s principal.

The 7-year-old girl, Miriam Monsonego, died in her father´s arms as medics tried to resuscitate her.

"He came on his motorbike, got off and shot a bullet in the air... Then he got out another gun and started shooting at everyone, at the children. He chased us into the school," Baroukh, a Jewish man living nearby who had come for morning prayers, told Reuters, declining to give his family name.

Military police reinforcements were rushed into the area and guards were deployed at mosques and synagogues in the region. In the United States, New York police ramped up security at synagogues and other Jewish institutions citywide.

Video surveillance footage showed the gunman bursting into the school and shooting one child at close range in the head, before fleeing on a motorbike, said Nicolas Yardeni, regional head of the French Jewish umbrella association, CRIF.

It was the worst anti-Semitic incident in France since August 1982, when six people were killed in a grenade attack and subsequent shooting at the Goldenberg restaurant in a Jewish neighborhood of central Paris. France´s 600,000-strong Jewish community is Europe´s largest.

Sarkozy and Francois Hollande, the Socialist opposing him in his uphill bid for re-election in May, both rushed to the scene.

"Barbarity, savagery and cruelty cannot win, hate cannot win. The republic is much stronger than all this," Sarkozy said, announcing a minute of silence in schools on Tuesday.

"One can imagine that the bloodthirsty madness was linked to racism," Sarkozy said, declaring he would suspend his campaign until Wednesday, when he would attend the soldiers´ funeral.

Sarkozy said the gun used in the school shooting was the same one used to kill the three soldiers by a lone gunman who also escaped on a motor bike. He said the terrorism alert in the region around Toulouse had been raised to scarlet, its highest level.

Some 120 investigators were working on a manhunt for the killer and had already identified the license plate of the motor bike used in the attack, police sources said. The gunman used a second gun when the first jammed, the Toulouse prosecutor said.

Police cordoned off the school, where well-wishers had begun to lay wreaths of flowers outside the bullet-marked walls as a line of police stood guard. Hearses arrived carrying the bodies of the victims for an overnight vigil attended by sobbing parents and relatives.

Hundreds of mourners in prayer caps gathered at the main mosque in Toulouse, a bustling university town which is a hub for Europe´s aerospace industry including aviation manufacturer Airbus. In Paris, thousands staged a silent evening march in central Place de la Republique, while political leaders joined a solemn remembrance ceremony at the grand synagogue.

"HORROR"

"I saw two people dead in front of the school, an adult and a child ... Inside, it was a vision of horror, the bodies of two small children," one father, searching for his son at the school among crowds of distraught parents and children, told RTL radio.

"How can they attack something as sacred as a school?"

As messages of condolence poured in from across Europe, representatives of France´s Jewish community voiced their solidarity. In the past decade, there has been a string of attacks on synagogues and Jewish schools, which educate some 30,500 children in France.

"I am horrified by what happened outside a Jewish school in Toulouse today. It has bruised by body and my soul," said Gilles Bernheim, France´s chief rabbi.

The Israeli embassy in Paris said the bodies of all four victims would be flown to Israel for burial as soon as possible at the request of their families.

"Today we had a savage crime in France that gunned down French Jews, among them children," Israeli Prime Minister Benjamin Netanyahu told reporters in Jerusalem. "I´m sure that Nicolas Sarkozy, the president of France, and his government will do their utmost to find the killer and we in Israel will do everything to help them in this task. "

Public prosecutor Valet said investigators were studying video evidence from the school shooting and the attack on Thursday in the nearby town of Montauban that killed two soldiers and left a third seriously injured.

The three men, aged between 24 and 28, were shot while in uniform as they tried to withdraw money from a cash machine close to the barracks of the 17th parachute regiment. A female witness told French television the masked attacker appeared to have a tattoo on his face when he lifted his visor.

A third soldier, aged 30, was killed the previous weekend in Toulouse. In the wake of the attacks, French media reported that two members of the 17th regiment had been expelled for neo-Nazism in 2008, prompting speculation of a racist motivation.

The shootings could thrust security back to the top of the agenda in a bitter electoral campaign that has been dominated by issues of taxation and immigration. "This is not just one school, Jews, or just one city which have been affected but all of France," Hollande said in Toulouse.

Stephane Rozes, head of CAP political consultancy, said the shootings were unlikely to have a decisive impact on the election outcome as all candidates had strongly condemned the violence, including far right leader Marine Le Pen.

Le Pen said politics and the election campaign should be kept out at times like this. "There is no more right or left, there is only the French people, wounded in its heart."

(Reporting by Guillaume Serries and John Irish in Toulouse; Leigh Thomas, Thierry Leveque, Nicolas Bertin, Lionel Laurent and Chine Labbe in Paris; Jeffrey Heller and Maayan Lubel in Jerusalem; writing by Daniel Flynn and Geert De Clercq; editing by Philippa Fletcher) (© Thomson Reuters 2012. 03/19/12)