French police have arrested a French jihadist on suspicion of shooting four people dead at the Jewish Museum of Belgium in Brussels.

Mehdi Nemmouche, 29, from the French commune of Roubaix on the Belgian border, was arrested in Marseille by customs officers after arriving on a bus from Amsterdam. The alleged killer was a former fighter in Syria and has been detained on charges of murder and attempted murder in association with a terrorist group.

Three people, including two Israeli tourists, were killed in the attack while a fourth later died from  injuries sustained. Police revealed that Nemmouche had a Kalashnikov machine gun, a pistol, a video camera and a blue cap on his person, similar to the items used by the killer in the museum attack.

It is also reported that Nemmouche was in possession of a series of newspaper articles on the Brussels museum attack. French President Francois Hollande congratulated the police and suggested that the alleged killer was arrested after a customs inspection because the bus had arrived from the Dutch city, where cannabis is easily obtained.

"The man was arrested as soon as he set foot in France," Hollande said. "We will fight them, we will fight them, we will fight them," the president said of French jihadists. "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."

Nemmouche was known to French counterterrorism police and was under surveillance after returning to France from Syria last year. He is now being interrogated by counterterrorism police in Levallois-Perret, near Paris.