The 29-year-old Frenchman arrested over the fatal shooting of three people at Brussels' Jewish Museum was radicalised during the last of his five stays in jail in France, a prosecutor said.
"During his last stay in jail he was noticed for extremist (Islamic) proselytism," Paris prosecutor Francois Molins said.
He said that the suspect, Mehdi Nemmouche, travelled to Syria only three weeks after he was freed in December 2012.
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The Police Federation chairman said officers were often "letting someone off with a warning and hoping for the best".
A total of 21 are also injured by a blaze which ripped through the upmarket 22-storey hotel on the Black Sea coast.