However, interior minister Claude Gueant told journalists “there is no known link” between those detained yesterday and Mohamed Merah, the 23-year-old Frenchman who claimed responsibility for shootings last week in Toulouse and Montauban.
Mr Sarkozy gave no details about the reasons for the latest arrests.
“It’s in connection with a form of Islamist radicalism,” the president said.
“There will be other operations that will continue and that will allow us to expel from our national territory a certain number of people who have no reason to be here.”
A police source said the anti-terrorist unit of the Criminal Brigade detained five men before dawn in Paris who had suspected links to an Islamist movement.
Weapons were also seized, said the official.
The other arrests took place in Toulouse, Marseille, Nantes and Lyon, the official said.
In Nantes, Mohammed Achamlane, the head of Forsane Alizza, a radical Muslim group that formed two years ago, was among the detained. French officials had banned the group in February.
Public order and security are high up on the agenda as Mr Sarkozy seeks re-election in the presidential poll later this month.
“It’s our duty to guarantee the security of the French people. We have no choice. It’s absolutely indispensable,” he said yesterday.
French Muslims have worried about a backlash after Merah’s attacks, and French leaders have urged the public not to equate Islam with terrorism.
However, concerns about radical Islam are high and on Thursday the government banned several Muslim clerics from entering France for a conference.