“This man wanted to bring the Republic to its knees,” President Nicolas Sarkozy of France said on Wednesday, but “the Republic did not yield.” He spoke in nearby Montauban at a funeral service for three soldiers that Mr. Merah said he had killed in the days leading up to Monday’s killings of a rabbi and three children at a religious school here.

The bodies of those killed at the school — Rabbi Jonathan Sandler, 30, a religious instructor; his two sons, Arye, 6, and Gabriel , 3; and Miriam Monsonego, 8, the daughter of the school’s principal — were flown to Israel where they were buried Wednesday in the sprawling cemetery known as Har Hamenuchot, or the Mount of Rest, in the Jerusalem hills. Rabbi Sandler was a French citizen; the children had dual French-Israeli nationality.

Before the burials, mourners packed into a sun-drenched courtyard, many of them men wearing the black clothes of ultra-Orthodoxy. French and Israeli dignitaries, including the French foreign minister, Alain Juppé, joined relatives of the victims there in eulogizing the innocents, their bodies wrapped in prayer shawls and a velvet cloth and laid out on stretchers before the small podium.

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Mr. Juppé said that the whole of France was in shock over the attack, adding, “Your pain is ours.”

While much about Mr. Merah’s past remained unclear or unverified, he seemed to be another example of the kind of homegrown terrorist, with a European nationality and passport, considered a major security threat in a period when Al Qaeda has largely disappeared as a coherent organization.

The authorities said they initially suspected both Mr. Merah and his brother Abdelkader, 29, who was known locally for his radical religious ideology and had been detained for questioning outside Toulouse on Monday.

Explosives were found in Abdelkader’s car on Wednesday, the police said, and Mr. Merah was tracked in part because his mother’s computer had been used to make contact with his first victim, a French soldier selling a motorbike online, whom Mr. Merah says he killed on March 11.

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Investigators tapped eight telephone lines beginning Monday evening. On Tuesday, they viewed surveillance tapes from the killings that showed the gunman, with what appeared to be a video camera strapped to his chest, seeming to film his actions as he coolly shot his victims. They also met with a motorcycle dealer who recalled a visit by one brother, which allowed them to identify the two as primary suspects in the case, Mr. Molins said.

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They were able to locate the two later that day, he said, and plans were made late in the night on Tuesday to arrest them, along with their mother. Investigators were not certain at that point which brother had been the gunman. It was not until Mr. Merah opened fired on the elite police agents sent to capture him that he became the prime suspect.

Police negotiators had hoped his mother would help persuade him to surrender, but she would not speak to the suspect, saying that her son had refused to listen to her in the past.

Given the national climate of fear, Mr. Sarkozy met with Jewish and Muslim leaders in Paris on Wednesday morning and called for restraint and solidarity among the populace. “We must be united,” he said in a brief address. “We must yield neither to easy falsehoods nor to vengeance.”

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Before meeting with Mr. Sarkozy, Richard Prasquier, the national head of the Crif, a prominent Jewish organization, said: “It is absolutely excluded that we confuse this character — and the Islamist, jihadist, Al Qaeda-linked movement he represents — and the Islam of France, which is a religion like all other religions.”

Mohammed Moussaoui, the president of the French Council for the Muslim Faith, who also met with Mr. Sarkozy, said, “These acts are in total contradiction with the foundations of this religion.” And the head of the Grand Mosque in Paris, Dalil Boubakeur, urged France not to stigmatize Muslims, saying “99.9 percent” are law-abiding and loyal citizens.

There was similar anxiety on the streets of Paris. Farouk, 25, who has a long beard and asked that his surname not be used, said that people in the North African Muslim community here “are disgusted with what has happened — it’s we who suffer, it’s we who will be criticized.” Racism, he said, “has a new face: Islamophobia, and it will be accentuated now.”

Said Meghani, 44, a professor of mathematics in Lille, said “I wish the European population would understand that Muslims themselves are also victims of terrorism and of radical Islam.” He was angry, he said, at Muslims who commit such crimes. “They use religion to spread their murderous ideology.”

Mr. Meghani said that Francee has a duty to “watch” people who “have come from Afghanistan or Pakistan,” but that France “should also take them and indoctrinate them,” as a preventive measure. “It is here where the state has failed.”

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The shootings of the paratroopers, who were attacked in separate episodes in Toulouse and Montauban, were not linked to their ethnic backgrounds, Interior Minister Claude Guéant insisted. The three dead soldiers were of Arab origin, and a black soldier is in critical condition.

Mr. Sarkozy had ordered the region’s security alert to “scarlet” — its highest level — for the manhunt. That is one step short of a formal state of emergency, giving security forces wide powers that include the authority to close some public places, to halt and search public transportation networks, and to deploy combined patrols of police officers and soldiers. The police were ordered to guard Muslim and Jewish schools and places of worship across the region.

Before the authorities said on Wednesday that their prime suspect claimed ties to Al Qaeda, many analysts had speculated that he had perhaps been motivated by extreme right-wing passions coinciding with the next month’s presidential election, and most of the candidates have suspended their campaigns.

In addition to Mr. Sarkozy, who is trying to draw voters from the far-right National Front Party, Wednesday’s funeral for the soldiers in Montauban was attended by several other candidates, including the Socialist frontrunner François Hollande and the National Front’s Marine Le Pen.