Appearing publicly for the second time since rioting began, Mr Chirac said the "re-establishment of order is for me an absolute priority... which has not yet been achieved."
"When the time comes and order has been established, it will be necessary to draw all the consequences from this crisis and do it with much courage and lucidity," the president told journalists after talks here with Spanish Prime Minister Jose Luis Zapatero.
Meanwhile, eight police officers were suspended pending results of an investigation into an alleged assault on a young man in a Paris suburb, the interior ministry said.
Calm returns
Calm gradually returned to French cities following introduction of a state of emergency and curfew as the government struggled to contain a wave of car-burnings, arson attacks and rioting mostly by young Arab and black residents of poor out-of-town estates.
Police spoke of a major reduction in violence overnight Wednesday, reporting 482 cars set alight across the country and 203 people arrested, compared to 617 cars torched and 330 arrests the night before.
At the peak of the trouble on Sunday night about 1,400 vehicles were burned and 395 people arrested across the country.
The easing-off came after the government decreed a state of emergency in much of the country on Tuesday, with curfews in some 30 towns and cities, where unaccompanied children under 16 were ordered to stay at home.
Commenting on the suspension of the police officers, an interior ministry spokesman said there was evidence that "two officers inflicted blows on the man in an illegal manner and that six others witnessed the incident."
The assault on Monday was filmed by a news crew from state-owned France 2 television channel, who have handed their footage to investigators, a police official said. France 2 broadcast the pictures late Thursday.
"A medical statement shows the man has superficial bruises on his forehead and his feet," the interior ministry said.
Sarkozy unrepentant
Interior Minister Nicolas Sarkozy said late Thursday on television he would not permit any police excesses.
"I took the decision at seven o'clock this morning to discipline the police officers," he said. "I will not accept any excesses by forces of law and order."
Curfews were lifted Thursday in seven out of 21 towns on the French Riviera, following a "clear improvement in the situation", the authorities said.
Mr Chirac, who has been criticised for taking a back seat, said it was time for "reflection, which I shall devote to explaining to my fellow citizens what my feelings are on this crisis and the means to remedy it."
"Whatever our origins we are all children of the republic. We can all claim the same rights but must of course all accept the same duties," he said.
Controversy also continued to surround a call by the tough-talking Mr Sarkozy for foreigners convicted of acts of violence during the troubles to be deported, a measure denounced by left-wing parties and campaigning groups as a breach of human rights.
On Tuesday, the government of Prime Minister Dominique de Villepin outlined a twin-track initiative to defuse the unrest, invoking a 50 year-old law that authorises curfews and house-to-house searches and at the same unveiling a classic package of social assistance to help the stricken areas.
Meanwhile Mr Sarkozy said on television Thursday he had no regrets about his inflammatory references to young troublemakers as "rabble," a remark that has caused a wave of protest and controversy.
"They are hoodlums and rabble, I insist on this and I stick to it," Mr Sarkozy said.
"When I say they are rabble, that's what they call themselves," the minister stressed. "Let's stop calling them youngsters. If you call hoodlums 'youngsters' you risk making generalisations about young people."
The violence wave was sparked by the accidental deaths of two teenagers electrocuted while hiding from police in an electrical sub-station.