Mr Villepin called for giving his controversial First Employment Contract (CPE) "a chance", and said that he "regretted" it was misunderstood.
"We must give the CPE a chance. A CPE completed and improved to answer everyone's concerns," Mr Villepin said following Saturday's protests in an interview with the youth magazine Citato, which will appear this week.
Meanwhile union and student leaders have given Mr Villepin an ultimatum to withdraw the CPE by Monday afternoon.
On Saturday thousands of opponents of the jobs plan took over the streets of Paris and other cities in at times violent demonstrations.
The march through the French capital ended in violent clashes between riot police and masked gangs, who hurled projectiles, set cars alight and smashed shop windows and telephone booths.
Police fired tear gas and made baton charges to disperse demonstrators at the Place de la Nation in the east of the city, and later in the Latin Quarter used water cannon to break up protesters trying to pull down a metal barrier blocking access to the historic Sorbonne University.
Police said they made 167 arrests in the clashes, which were the worst since tensions over the youth jobs contract erupted two weeks ago.
A total of 34 police officers and 18 demonstrators were injured, though none seriously.
Campaign organisers will meet on Monday evening to assess the government's response to their threat of a fresh escalation via a general strike.
Bernard Thibault, head of the powerful General Labour Confederation (CGT), said that "if nothing moves we will propose preparing a day of general work stoppages in the coming days. Conditions are such that it should be a success."
Mr Villepin’s jobs plans amount to an open-ended contract for under 26-year-olds that can be terminated without justification in the first two years.
The CPE is meant to lower France's chronically high youth unemployment rate by offering employers greater flexibility and was conceived in the wake of last November's riots in high-immigration suburbs, where fewer than one young person in two has a job.
But its proposed implementation has sparked a growing wave of opposition with unions, students and left-wing parties calling the CPE a charter for employer exploitation and a breach of France's hard-won labour rights.
President Jacques Chirac has urged the two sides to open talks, but an increasingly buoyant opposition says that abandonment of the CPE is a precondition for negotiations.
The conflict over the youth jobs plan is Mr Villepin's most serious crisis since he took office 10 months ago.
Political analysts say that his political future as a possible contender to replace Mr Chirac in next year's presidential election is at stake.