His comments came as arsonists struck in several cities in France.
Youths, mostly French-born children of Arab and black Africans, set ablaze nearly 1300 vehicles and torched businesses, schools and symbols of French authority, including post offices and provincial police stations, on the 10th consecutive night of unrest.
Police spokesman Patrick Hamon made 349 arrests nationwide, he said.
Chirac spoke on Sunday after a security meeting of his top ministers.
"The law must have the last word," Chirac said in his first public address on the violence. Those sowing "violence or fear" will be "arrested, judged and punished".
"The absolute priority is restoring security and public order," he said. He said security measures would be reinforced.
Chirac had faced criticism from opposition politicians for not publicly speaking about France's worst civil unrest in more than a decade. His only previous comments came through a spokesman.
Worst civil unrest
From an outburst of anger in suburban Paris housing projects, the violence has fanned out into a nationwide show of disdain for French authority from youths and minorities, mostly the children of Arab and black Africans angered by years of unequal opportunities.
"The law must have the last word"
The violence soon spread to the well-guarded French capital. Police said 35 cars were torched, mostly on the city's northern and southern edges.
In central Paris, petrol bombs damaged three cars near Place de la Republique. Residents reported a loud explosion and flames.
"We were very afraid," said Annie Partouche, 55, who watched the cars burning from her apartment window. "We were afraid to leave the building."
Buildings were set ablaze in a
10th night of violence
For a second night, a helicopter equipped with spotlights and video cameras to track bands of marauding youths combed Paris suburbs and small teams of police chased rioters speeding from attack to attack in cars and on motorbikes.
"What we notice is that the bands of youths are, little by little, getting more organised," arranging attacks through mobile phone text messages and learning how to make gasoline bombs, Hamon said.
Police found a petrol bomb-making factory in a derelict building in Evry south of Paris, with more than 100 bottles ready to turn into bombs, another 50 already prepared, as well as fuel stocks and hoods for hiding rioters' faces, senior Justice Ministry official Jean-Marie Huet told The Associated Press.
Police arrested six youths, all under 18.
The discovery on Saturday night, he said, shows that petrol bombs "are not being improvised by kids in their bathrooms".
Several thousand vehicles have
already been torched in France
Police say copycat attacks are fanning the unrest, but have no evidence of separate gangs coordinating. Officials say older youths, many already with police records, appear to be teaching younger teens arson techniques.
Unrest extended west to Normandy and south to Nice and Cannes on the Mediterranean coast. There were attacks in or around the cities of Lyon, Lille, Marseille, Strasbourg.
Thousands of vehicles burnt
In all, 3300 buses, cars and other vehicles have been incinerated in 10 nights, said Hamon, the police spokesman.
In Evreux, 100km west of Paris, five police officers and three fire fighters were injured in clashes with youths who destroyed at least 50 vehicles, shops and businesses, a post office and two schools, authorities said.
"Rioters attacked us with baseball bats," said Philippe Jofres, a deputy fire chief, told France-2 television. "We were attacked with pickaxes. It was war."