French President Jacques Chirac has urged ministers to start immediate talks on a controversial new labour law intended to curb youth unemployment.
The Paris clashes continued through Thursday evening
His comments follow the arrest of at least 300 people across France, when mass protests against the law ended in unrest in Paris and other cities.
Mr Chirac said the law was important for fighting joblessness and called for further protests to be peaceful.
More than 50 police officers were injured in the clashes.
Interior Minister Nicolas Sarkozy blamed the violence on a group of delinquents from the far left and far right, but said the vast majority had demonstrated peacefully.
At least 250,000 people took part in the protests across the country.
The architect of the law, Prime Minister Dominique de Villepin, said he was open to dialogue and would meet university presidents to seek solutions.
But he refused to withdraw the law, which he said was essential in combating youth unemployment.
Mr Chirac called on all concerned to show "responsibility" to avoid a repeat of the violence.
"You know the government is ready for dialogue and I hope this will start as quickly as possible," he said.
But he continued to defend the bill.
"It brings opportunities and new guarantees for young people in difficulty," he said.
Students fear the First Employment Contract (CPE), which passed into law last week, will erode job stability in a country where more than 20% of 18- to 25-year-olds are unemployed - more than twice the national average.
Mr Villepin's government proposed the law to help youths in the French suburbs who took to the streets last year, many unhappy with the lack of employment opportunities.
Echoes of 1968
The worst violence on Thursday was in Paris, where riot police fired rubber bullets and tear gas. Unrest was also reported in some of the other 80 cities holding rallies.
The Paris march, which police said was attended by 30,000 but which organisers put at 120,000-strong, was mainly peaceful.
However, a group of about 300 masked protesters threw missiles at police, who responded with tear gas and rubber bullets.
Clashes went on into the evening and the interior ministry said there had been about 150 arrests in Paris, along with at least 50 more elsewhere.
The BBC's Caroline Wyatt in Paris says the worry for the French government is that, as in May 1968, French students are expressing wider disenchantment with a government that is seen as remote and out of touch.