(Reuters) - French police stepped up the search on Tuesday for a gunman who filmed his carnage as he shot dead three children and a rabbi at a Jewish school, fearing the killer could strike again.

Officials believe the scooter-riding gunman is a trained marksman with "extremist" views who may also be responsible for last week´s shootings of three soldiers of North African origin.

France´s President Nicolas Sarkozy has said racism appeared to be the motivation for Monday´s school attack, which came just five weeks before the first round of the presidential election.

Racist and anti-Semitic attacks are not uncommon in France.

Immigrants and Islam have been major themes of the campaign as Sarkozy tries to win over the voters of far-right leader Marine Le Pen. Analysts say the shootings could transform the election debate and possibly tone down populist rhetoric.

"We will track down this monster," Foreign Minister Alain Juppe said of the killer on France 2 television. "We will find him, bring him to justice and punish him."

France is home to the largest Jewish and Muslim communities in Europe and has a history of attacks on both groups, but Monday´s shooting was the most deadly anti-Semitic attack on French soil in nearly 30 years.

The police tightened security at religious sites, raised the terror alert in the southern town to the highest possible level and talked to gun clubs in an effort to track down the killer.

"It would be surprising if he stops now," one police officer involved in the investigation told Reuters.

Surveillance tapes at the school showed the gunman recorded his shooting spree with a small video camera around his neck.

He is also the prime suspect in the killing of three paratroopers in two separate shootings last week in Toulouse and the nearby town of Montauban.

"This shows a profile of the murderer as someone who is very cold, very determined, with precise gestures, and therefore very cruel," Interior Minister Claude Gueant said.

In each attack, the gunman arrived on a stolen Yamaha scooter and used a Colt 45 handgun. His face was hidden by a motorcycle helmet during the attacks.

The three dead soldiers included two members of the 17th parachute regiment. Police have interviewed three former soldiers expelled from the regiment for neo-Nazi activity in 2008, but a police source told Reuters on Tuesday they had been ruled out of the investigation.

"GETTING READY FOR PRAYERS"

At the entrance of the Ozar Hatorah Jewish school in Toulouse, a five- floor brick building in a leafy residential neighborhood, residents and parents left floral tributes and candles in memory of the victims.

A child who survived the attack spoke of his sheer terror as the shots rang out through the school.

"We were getting ready for prayers when the principal stormed in and screamed that there was a shooting. I panicked and fled to the old canteen and heard the shots, but saw nothing," an 11-year old boy told France Info radio.

"I thought he was going to come in any minute and finish us all. Then I waited and waited and then my daddy came to get me."

Schools all over France observed a minute of silence.

"This has happened in Toulouse, in a religious school with children from Jewish families, but it could have happened here. The same killer could have come here, these children are exactly like you," Sarkozy said, attending the silent vigil in a Paris secondary school.

The bodies of the four victims, who hold dual French-Israeli nationality, will be repatriated to Israel on Tuesday night, Joel Mergui, the head of a Jewish religious organization, said.

The Israeli embassy identified the victims as Jonathan Sandler, 30, his children Gabriel and Arieh, aged four and five, and Myriam Monsonego, seven.

RACIAL TENSION

France´s Jewish umbrella group Crif welcomed the decision by political parties to suspend their election campaigning until Wednesday out of respect for the victims. Analysts said the killings would change the election debate.

"The tone of the campaign cannot go back to what it was," said Dominique Reynie, head of Fondapol politics institute.

"The campaign was dominated by an aggressive tone and a strong degree of populist rhetoric. This rhetoric will cease because there will be voter demand for healing."

France´s far-right leader Marine Le Pen is running third in the race for the presidency and this has helped to draw issues of race and immigration into the election campaign.

The centre-right Sarkozy has tried to attract her voters with a pledge to halve immigration and criticism of halal slaughter as he lags Socialist Francois Hollande in voting intentions polls.

Some analysts said there would be a discussion about whether Sarkozy has stirred feelings that led to the attack.

"There will be more debate, notably on whether the tension created in society by Nicolas Sarkozy and the UMP (ruling party) has not somehow provoked or facilitated this type of violence," said L´Express magazine editor-in-chief Christophe Barbier.

Juppe said the campaign could not have triggered the shooting.

"Anti-Semitism exists in France, we have fought it for years," he said.

"Nobody should try to benefit in any way from this drama, which is in no way linked to the electoral campaign."

(Additional reporting by Geert De Clercq, Emmanuel Jarry and Marine Pennetier; writing by Geert De Clercq; Editing by Anna Willard) (© Thomson Reuters 2012. 03/20/12)