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 40-second video found in his possession along with a Kalashnikov and a handgun.
Paris prosecutor François 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.
Instead Nemmouche later "filmed his weapons and said he carried out the attack against the Jews in Brussels", prosecutor Frederic Van Leeuw told a simultaneous press conference taking place in the Belgian capital.
However Van Leeuw added: "We can't guarantee that it is his voice heard on the recording."
A day later, on Monday, Interior Minister Bernard Cazeneuve told Europe 1 radio police had carried out a series of raids on jihadists in France. He didn't say if the killings and the arrests are related.
"As I speak recruiters for jihad in Syria are being arrested in the Ile de France region (Paris) and in the south of France. There have been four arrests. We want the hunt to be thorough, we don't want to leave any opportunity to the terrorists," Cazeneuve said.
In regards to the Brussels shooting, 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".
He described Nemmouche as a "battle-hardened lone wolf" who left for Syria on December 31st, 2012, just three weeks after being released from prison. He returned to Europe in March this year and appears to have fought alongside the ISIL fighters.
The French prosecutor said Nemmouche 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."
President Francois Hollande said the suspect was "arrested as soon as he set foot in France".
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.
An Israeli couple and a Frenchwoman died on the scene and a 24-year-old Belgian man was left clinically dead.
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".
Molins said Nemmouche said little during the interrogation, describing himself as a homeless man who lived in Belgium.
He is being questioned by the DGSI who can hold him for up to 96 hours, until Tuesday, or 144 hours, to Thursday, if investigators invoke an imminent terrorist threat.
His family meanwhile reacted with horror, describing him as taciturn but harmless.
"He is nice, intelligent, educated and has done a year at university," Nemmouche's aunt told reporters, adding that the family was "very shocked."
She said Nemmouche had been raised in a foster home and then by his grandmother, adding that the family lost contact with him after he was sent to prison.
"He never went to the mosque or spoke of religion," she said.
The attack was the first such incident in more than 30 years in Belgium and has revived fears of a return of violent anti-Semitism to Europe.
The European Jewish Congress has called for greater security at Jewish institutions and tougher legislation for dealing with anti-Semitic crime.
Some 40,000 Jews live in Belgium, roughly half in Brussels and the remainder in the port city of Antwerp.
Nemmouche's past also stands to reignite a row in France over the monitoring of those who leave to country to fight in Syria.
Belgian Prime Minister Elio Di Rupo called for closer European cooperation to fight jihadists including tighter monitoring to "avoid such tragedies from being reproduced".
Hollande meanwhile said: "The government is mobilized to track down jihadists and prevent them from causing more harm."
According to the latest figures, some 780 people have left France to fight with jihadists in Syria.