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Mehdi Nemmouche was detained on Friday (local time) after a random check at a bus terminal in the French city of Marseille showed he was carrying a Kalashnikov rifle, another gun and ammunition similar to those used in the shooting last weekend, French and Belgian prosecutors said.
Paris prosecutor Francois Molins told reporters Nemmouche had been carrying a video where a voice resembling his own claims responsibility for the shootings.
European governments have become increasingly worried that citizens going to fight in Syria will import Islamist militancy on their return.
Nemmouche served five jail terms in France before spending most of 2013 in Syria, Molins said.
"During his last stay in jail, he was noticed for extremist (Islamist) proselytism," Molins said. "He spent over a year in Syria, where he seems to have joined the ranks of combatant groups, jihadist terrorist groups."
Belgian federal prosecutor Frederic Van Leeuw told a separate news conference that the Kalashnikov had been wrapped in a flag with the inscriptions of the Islamic State of Iraq and the Levant (ISIL), an ultra-conservative militant group reconstituted from an earlier incarnation of al Qaeda and active in Syria and Iraq.
An Israeli couple and a French woman were killed when a man entered the Jewish Museum in the centre of the Belgian capital on May 24 and opened fire with a Kalashnikov. A Belgian man remains in critical condition in hospital.
A 30-second video clip from the museum's security cameras released by police showed a man wearing a dark cap, sunglasses and blue jacket entering the building, taking a rifle out of a bag and shooting into a room before calmly walking out.
The attack evoked memories of the killing of four Jews in 2012 at a school in France by Mohamed Merah, a gunman inspired by al Qaeda.
After Nemmouche's arrest was announced, President Francois Hollande said France was determined to do all it could to prevent radicalised youths carrying out attacks.
"We will monitor those jihadists and make sure that, when they come back from a fight that is not theirs, and that is definitely not ours, ... they cannot do any harm," he told reporters. "We will fight them, we will fight them, and we will fight them."
He said about 700 French jihadists were either in Syria or had returned to France after fighting there, a major concern in a country that is home to both Europe's largest Jewish and Muslim communities, the latter mostly of North African origin.
France announced new policies in April that aimed to prevent young Muslims becoming radicalised and to stop French citizens joining the Syrian civil war.
Nemmouche is being held on suspicion of murder, attempted murder and possession of weapons, all in the context of terrorist activity, Molins said, adding that the suspect had made no comment on the accusations.
Soulifa Badaoui, who has worked as a lawyer for Nemmouche the suspect in the past, told BFM TV that he was "not observant at all" at the time.
Belgian federal magistrate Erik Van der Sypt told Reuters that Belgium would seek Nemmouche's extradition from France.
European Jewish Congress President Moshe Kantor urged more action to stop hate crimes.
"...For too long, authorities in Europe have acted speedily after the fact," he said in a statement. "It is now time for all ... to make the prevention of these vicious crimes a top priority."
Security around all Jewish institutions in Belgium was raised to the highest level after the shooting, and French authorities also stepped up security after two Jews were attacked the same day as they left a synagogue in a Paris suburb wearing traditional Jewish clothing.
About half of Belgium's 42,000-strong Jewish population live in Brussels. France's Jewish community is the largest in Europe at some 550,000, though violence such as the 2012 school murders and economic woes have prompted an increase in emigration to Israel or elsewhere.