Mehdi Nemmouche, 29, who was arrested by customs agents on Friday on arrival in the southern French city of Marseille, is believed to have recorded the claim in a short video found in his possession along with a Kalashnikov and a handgun.
Paris prosecutor Francois Molins said the "repeat offender" explains in the film that he had attached a GoPro camera to his bag to record his shooting rampage, but it had not worked.
However Van Leeuw added: "We can't guarantee that it is his voice heard on the recording."
Molins said the suspect, who arrived in France on a bus from Amsterdam via Brussels, was also carrying a "white cloth" carrying an inscription in Arabic of the Islamic State of Iraq and the Levant (ISIL) -- Syria's most extremist group -- and the words "Allah is great".
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The French prosecutor said Nemmouche was converted to radical Islam during five stints in prison, adding the suspect called for "collective prayers while he was let out of his cell for exercises."
A judicial source said he had been detained on suspicion of murder and attempted murder in connection with a terrorist enterprise.
Nemmouche, originally from Roubaix in northern France, is believed to have travelled to join Islamist fighters in Syria in 2013, and was known to the French domestic intelligence agency DGSI, said one source close to the case.
A lone gunman entered the Jewish museum in the heart of Brussels last Saturday, removed an automatic rifle from a bag and opened fire through a door before making an exit.
Sources confirmed that Nemmouche was carrying a Kalashnikov automatic rifle and a gun with ammunition in his luggage.
"These weapons were of the type used in Brussels," said one source. Another source close to the investigation said that there were many elements "consistent with the shooting in Brussels".