"We're at a time when a bit of national unity around our security forces, around those who are really struggling would be a good thing for the country," Griveaux added.
An estimated 75,000 demonstrators, most of them peaceful, were counted across the country on Saturday, the interior ministry said. The number was well below the first day of protests on November 17, which attracted around 282,000 people, and also down from the 106,000 who turned out last Saturday.
Interior Minister Castaner attributed the violence to "specialists in sowing conflict, specialists in destruction".
He did not rule out imposing a state of emergency -- a demand made by the police union Alliance -- declaring: "Nothing is taboo for me. I am prepared to examine everything." Two people have died and dozens have been injured in the rallies, which opinion polls suggest still attract the support of two out of three French people.