In Paris, first arrest of Islamist suspects since start of Mali war
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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.
Police have stopped several individuals trying to travel from France to the Sahel, Valls said. The Sahel is the vast swath of semi-arid territory stretching from Senegal in west Africa to Eritrea in the east - and has been identified as a base for traffickers and Islamist militants.
He said a "handful" of French nationals had already joined Al Qaeda-linked groups.
"There is no direct threat, but there are threats on the Internet, on social networks, calling on people to wage war, to attack French interests," Valls said.
France has tightened security in public buildings and on public transport, although it has kept its security alert level at red, signifying "probable threats", one down from the scarlet level which means "definite threats".
Highlighting the threat overseas, Paris has raised its travel warning for its citizens across the Muslim world.
The embassy in Tunis on Monday confirmed that a French school in the Tunisian capital had been sprayed with graffiti warning of reprisals after France's intervention in Mali.
Additional reporting by Nicolas Bertin, John Irish and Vicky Buffery; writing by Nicholas Vinocur and John Irish; editing by Jon Boyle.