Following an emergency meeting with top security advisers, Mr Chirac made his first public statement since the rioting began on October 27 in working class immigrant neighbourhoods.
"Those who want to sow violence of fear, they will be arrested, judged and punished," the president vowed.
But he also noted "respect for all, justice and equal opportunity" were needed to end France's worst unrest in nearly four decades.
Unrest has now flared in up to 200 city suburbs and towns across France, including Marseille, Nice, Lille, Bordeaux and Montpellier, police said.
Arsonists set fire to cars and trash cans in the cities of Nantes, Orleans and Rennes, and youths clashed with police in the southern city of Toulouse.
Police in Toulouse said they had to use tear gas grenades to push back a mob throwing stones and bottles.
"These individuals seem to be looking for contact with police, and they are attacking us, unlike during the other nights," a senior officer told news agency AFP.
Thirty police officers were hurt, two of them seriously, when they were shot at the Paris suburb of Grigny on Sunday.
Two riot squad officers hit by buckshot fired from pistols and hunting rifles were hospitalised, while the 27 others were treated on the spot.
A school and a kindergarten were set on fire in the same region, police said, adding that 30 people were arrested.
At an emergency meeting government ministers "took a certain number of decisions to bolster the action of police and the courts”, Mr Chirac said.
Prime Minister Dominique de Villepin, who attended the meeting with Interior Minister Nicolas Sarkozy, Defence Minister Michele Alliot-Marie and the ministers for justice, the economy and education, said more police would be deployed where troubles flared.
There will be "a reinforcement of security forces anywhere in the country it is necessary. We will not accept any lawless zone," he said.
The renewed violence, which has already raged on the outskirts of Paris and many of France's other major cities, has continued for 11 days despite the deployment of thousands of police.
More than 800 people have been arrested and 3,500 vehicles torched, mainly in the working-class, high-immigration suburbs of Paris that are at the centre of the troubles.
Most of those arrests and arson attacks occurred over the weekend.
Fifty-one cars were destroyed or damaged in central Paris overnight on Saturday, and 30 youths were arrested, many of them while they were preparing fire-bombs.
In a disturbing development 16 police and fire officers were hurt when a 200-strong crowd of youths, some armed with baseball bats, attacked police units in the western town of Evreux.
A police chief, Frederic Aureal, said his officers were encountering an unprecedented hostility from gangs, which he described as "prepared, structured, armed".
"We have come face-to-face with people who have attacked us with picks, petanque balls, many Molotov cocktails," he said.
In a sign of organisation behind the riots, police overnight Saturday discovered a petrol-bomb factory south of the capital with 50 bottles ready for use.
Police helicopters fitted with cameras and searchlights are being used to pursue youths who start fires then race away on scooters.
Officers have also started breaking down doors in public housing estates to get offenders.
Injuries reported
So far, no one has been killed in the unrest, which was sparked by the electrocution deaths of two teenagers who hid in an electrical sub-station in north-eastern Paris to escape a police identity check.
But at least two people have been badly burnt by Molotov cocktails: a fireman, and a handicapped woman unable to get off an ambushed bus.
A 61-year-old was also in a coma after being hit by an assailant in a public housing estate, and a South Korean female TV reporter was kicked unconscious by assailants in a northern suburb on Saturday.
Youths, in interviews, have boasted that they were intensifying the violence because of a sort of "competition" between gangs from different suburbs to get media attention.
They have also expressed anger at Minister Sarkozy, who described delinquents in the suburbs as "rabble" and vowed to clean up crime in the neighbourhoods "with a power-hose."