Toulouse (CNN) -- French police had no grounds on which to arrest gunman Mohammed Merah before he carried out three attacks in which seven people died, Prime Minister Francois Fillon told French radio station RTL Friday.
Merah, 23, who was shot dead by special forces Thursday after a siege lasting more than 30 hours in the southwestern city of Toulouse, was wanted in the killings of three French paratroopers, a rabbi and three children ages 4, 5, and 7.
Merah, a French citizen of Algerian descent, had been put under surveillance after trips to Afghanistan and Pakistan, officials have said, leading commentators to ask why he was not stopped sooner.
He claimed to have attended an al Qaeda training camp, according to Paris prosecutor Francois Molins, and was on the U.S. no-fly list for that reason, a U.S. intelligence official said.
And Toulouse lawyer Eric Mouton, acting for a woman named only as Aicha, to protect her privacy, told CNN she filed a complaint against Merah in 2010 over alarming behavior Merah displayed toward her children.
Aicha claimed that Merah had beaten up her daughter, 19 at the time, and held her son, 15, against his will in a room for several hours, forcing him to watch videos of violent combat and of people's throats being slit.
Mouton said he would meet with Toulouse prosecutor Michel Valet later Friday to discuss the case. It is not known if any action was taken against Merah at the time.
Fillon defended the police and intelligence services, saying they had done a remarkable job in finding the killer within 10 days of the first attack, on March 11.
Fillon acknowledged that some questions should be asked, particularly with regard to surveillance.
But, he said, "there was no single element" that would have allowed the police to arrest Merah before the killings began.
"We don't have the right in a country like ours to keep under permanent surveillance without a judicial decision someone who has committed no offense," he told RTL. "We live in a country under the rule of law."
Crowds gathered in a square in central Toulouse at noon Friday to remember those killed in the attacks.
Toulouse Mayor Pierre Cohen called the rally in solidarity with the families of the victims and as a demonstration of unity against anti-Semitism and racism, CNN affiliate BMF-TV reported.
CNN iReporter Henry Krisch said the mood at the commemoration was "eerily silent and depressed," as the names of the seven dead were read out and a minute's silence was held.
Meanwhile, investigators carrying shovels, metal detectors and hammers re-entered Merah's apartment Friday, continuing their search of the premises.
A police cordon surrounding the property was removed in the afternoon, exposing the messy aftermath of the gun siege to those at the scene.
The first floor balcony from which Merah jumped, still firing, before being shot in the head, has been boarded up. Bullet holes pock the walls and nearby cars, and broken glass lies scattered around.
Elizabeth Allannic, a spokeswoman for the Paris prosecutor, said the detention of Mohammed Merah's mother, brother and his brother's girlfriend had been extended Friday.
Police tracked Merah down via his mother's computer IP address, which was apparently used to respond to an ad posted by the first victim, officials said. Interior Minister Claude Gueant initially told reporters it was the IP address of Merah's brother that led investigators to him.
Fillon said the French domestic intelligence service, the DCRI, had done its job "perfectly well, it identified Mohammed Merah when he traveled to Afghanistan and Pakistan, it questioned him and it monitored him, he was under surveillance, on a list, and it was thanks to that listing that he was identified.
"It watched him for the necessary period, and it led to the conclusion that there was no indication or trace that Mohammed Merah was a dangerous man."
Investigations will determine whether Merah acted alone, the prime minister told RTL. He added: "We must not mix religious fundamentalism with terrorism."
French President Nicolas Sarkozy vowed increased legal measures to punish those who pursue extremist activities online or travel overseas for indoctrination and training.
He spoke Thursday as campaigning resumed for the French presidential election, with the first round of voting due next month.
Rival candidate Francois Hollande, appearing at a rally Thursday night, said questions will have to be asked about the Merah case, French media reported.
Earlier, French Foreign Minister Alain Juppe told radio network Europe 1 that "light must be shed" on events leading up to the shootings by Merah.
"I understand that one can ask whether there was a failing or not. As I don't know if there was a failing, I can't tell you what kind of failing, but light must be shed on that," Juppe said.
The day after his third and final attack, on a Jewish school, Merah was tracked down to an apartment in Toulouse, where a siege began in the early hours Wednesday.
It finally came to a bloody end Thursday morning, when Merah emerged from a bathroom in his apartment and fired more than 30 shots at police who had burst in to end the standoff, Molins said.
Merah then jumped out a window onto a balcony, still shooting, and was found dead on the ground, officials said.
He died from a gunshot wound to the head, Molins said.
After Merah's death, Sarkozy said everything had been done to bring him to justice alive but security forces could not be exposed to further risk.
Authorities said the young man cited a variety of reasons for the killings, including the missions of French troops abroad, the oppression of Palestinians and France's ban on the wearing of Islamic veils.
After Merah was killed, police found video he had recorded of the attacks, ammunition and ingredients for explosives, Molins said.
In the video of the first shooting of a French soldier in Toulouse, Merah told the soldier, "You kill my brothers, I kill you," Molins told reporters. Another video shows Merah gunning down two more French soldiers in Montauban. He is heard saying "Allahu Akbar," or "God is great," Molins said.
Gueant said Merah had been under surveillance by French intelligence for years.
He had "already committed certain infractions, some with violence," Gueant said.
Merah was sentenced 15 times by a Toulouse juvenile court when he was a minor, Molins said. The charges mostly involved theft.
In the first shooting on March 11, Imad Ibn Ziaten, a paratrooper of North African origin, arranged to meet a man in Toulouse who wanted to buy a scooter Ziaten had advertised online, the interior minister said. The victim said in the ad that he was in the military.
Four days later, two other soldiers were shot dead and another injured by a black-clad man wearing a motorcycle helmet in a shopping center in the city of Montauban, about 50 kilometers (30 miles) from Toulouse.
In the attack at the private Jewish school Ozar Hatorah on Monday, a man wearing a motorcycle helmet and driving a motor scooter pulled up and shot a teacher and three children -- two of them the teacher's young sons -- in the head. The other victim, the daughter of the school's director, was killed in front of her father.
Police said the same guns were used in all three attacks.
CNN's Diana Magnay, Saskya Vandoorne, Anna Prichard and Alex Felton contributed to this report.