Nemmouche claimed responsibility for the attack "on the Jews".
Muslim violence has become the main reason for diminishing Jewish population in Europe.
Mehdi Nemmouche, the Brussels Jewish Museum killer, is only the latest in a long series of Muslims carrying on their religion's call for violence against Jews.
An Israeli couple and a French woman were killed on May 24 when a man entered the Jewish Museum in busy central Brussels and opened fire with a Kalashnikov. A Belgian man remains in critical condition in hospital.
French police have arrested a 29-year-old man suspected of involvement in the shooting deaths last weekend of three people at the Jewish Museum in Brussels, an attack that stoked fears of growing anti-Semitic violence in Europe.
Mehdi Nemmouche, a French citizen, was detained in the southern French city of Marseille on Friday and had a Kalashnikov assault rifle and another gun with him.
French media reported that he was suspected of having stayed in Syria with Islamist jihadist groups last year.
Speaking at a press conference on Sunday, Belgium's federal prosecutor said police had seized a video showing Mr Nemmouche claiming responsibility for the attack "on the Jews".
He said "all European countries" were facing a terrorist threat from people returning from the war in Syria.
The suspect, who was known to French security services as a jihadist volunteer in Syria until last year, is refusing to answer questions, police sources said.
A pennant bearing the name of the jihadi group the Islamis State of Iraq and the Levant was also found, Molins said.
Despite the claims that he was too amateurish to be Al Qaeda, Mehdi Nemmouche appears to be aligned with Al Qaeda in Iraq or its current name, ISIL or ISIS.
I believe that this would be the first Al Qaeda in Iraq attack in Europe.