Student and employee unions have given Dominique de Villepin, the prime minister, until Monday night to withdraw the measure, which is designed to increase hiring among the youth but seen by critics as an erosion of workers' rights that will not produce solid jobs.
"If this momentum continues, I think we will quickly get the withdrawal" of the measure, Bernard Thibault, head of the powerful CGT union, said on Sunday on France-Inter radio.
He said a one-day national strike was possible if the government stuck to its guns.
Protesters have urged Jacques Chirac, the president, to block the law, expected to take effect in April. Sixteen universities are on strike over the measure, and dozens of others have been disrupted.
Police said on Sunday that 52 people were injured - 18 of them demonstrators - in violence after the Paris protests a day earlier, with one protester hospitalised with heart problems.
First Jobs Contract
A total of 167 people were arrested, with 70 of them detained for questioning, police said. Cars and bus shelters were damaged in Saturday's violence along with 10 shops, including a McDonald's fast food restaurant and the entrance to a Gap clothing store.
Unions gave Villepin until Monday
night to withdraw the measure
"When youths take to the street, you don't know what can happen," said Julien Dray, the spokesman for the opposition Socialist Party. "By digging in its heels, the government is creating the conditions for troubles (that can have) dramatic consequences," he told Radio-J.
Dray said the government should withdraw the law.
Organisers of Saturday's nationwide protests put the number of participants at 1.5 million. Police, however, said a half-million people took part in cities around France. It was the second demonstration in three days and the biggest show yet of the country's escalating anger over the law.
The so-called First Jobs Contract, intended for those under 26 with little chance of finding a good job, is meant to encourage employers to hire because they can more easily fire. In effect, the law allows for dismissal within the first two years of employment without justification.
The French work code contains rigorous standards for firing employees. But Villepin hopes to use the measure to lower the 23% unemployment rate among the nation's youths, a figure that rises to about 50% in depressed suburban neighbourhoods where unrest erupted last year, fueled by discrimination and joblessness.
Students clashed with police
outside the Sorbonne university
On Saturday night, students protesting against the law clashed with police outside the Sorbonne University.
Police fired tear gas to disperse skirmishing youths at the end of the march in eastern Paris. They turned water cannons on the hundreds of protesters, who then moved across town.
"Liberate the Sorbonne!" youths shouted.
Riot police stormed the Sorbonne a week earlier to dislodge occupying students. The landmark institution in the heart of the Latin Quarter, the student neighbourhood, now stands behind elaborate barricades and has become a symbol of the protests.
Protest organisers have urged Chirac not to sign the law, as he must do for it to take effect.
They have demanded an answer by Monday - when unions plan to meet to decide a course of action.