"It's being accused of wanting to occupy Muslim territory and that could clearly push some individuals to take action, or encourage others to build up a network," she told Reuters.
Three of the four men arrested on Tuesday were Franco-Congolese and one was Malian, according to police sources.
Mr. Vall, the interior minister, said the arrests had come after a long investigation into Al Qaeda recruitment rings led by Mr. Trevidic.
"There is an operation ongoing in the Paris region, conducted by the DCRI [domestic security service], which comes after the arrest of an individual a few months ago on the border between Mali and Niger," he told BFM TV.
That man was a Franco-Congolese social worker named Cedric Lobo, 27, who was arrested in Niamey, the capital of Niger, while trying to reach the historic Malian city of Timbuktu to join the rebel group known as Al Qaeda in the Islamic Maghreb (AQIM), the source said.
He was subsequently extradited to France, where he was charged with planning attacks and remanded in custody.
French nationals drawn to violent militant groups had a number of points in common, said Valls, who has taken a hard line on law and order and has warned that France is facing an "enemy from within."
"The profiles are often individuals that have had problems with the law, been involved in drug trafficking, and have sometimes converted to radical Islam either in prison, through the Internet or by travelling overseas," Valls told reporters.
French anti-terrorism judges have opened a number of preliminary investigations in the past year into individuals suspected of links to what they say are Malian terrorist cells.