French Prime Minister Dominique de Villepin said Saturday that he was ready to meet the youth's two major concerns over job via dialogue -- the two-year trial period and conditions of the rupture of the job contract.
"I hope that through dialogue we can find a solution quickly," he said after meeting several student representatives.
"I therefore want to see student organizations next week to make headway with them on all these points," he said.
While major student organizations declined to meet Villepin on Saturday, trade unions have prepared a new round of strikes and demonstrations for next week.
Bernard Thibault, secretary general of the biggest French trade union, the CGT, called for a "large mobilization in France" for new demonstrations and national strikes planned for next Tuesday.
"We are in a process and we have to continue. It is out of the question to abandon the fight now," he said on French radio.
According to the CGT, 135 demonstrations will be held next Tuesday throughout France, especially in Paris, Marseille in the south, Lille in the north and Lyon in the southeast.
The French parliament adopted the CPE two weeks ago, which, sponsored by Villepin, encourages employers to hire young people under 26, with an open-ended two-year contract that could be terminated without explanation.
On Saturday French Interior Minister Nicolas Sarkozy, president of the right-wing ruling party UMP (Union for a Popular Movement), also called for "compromise" at a meeting of his party.
"To be able to imagine a compromise, it's to have courage and be useful to France -- that's what the UMP wants and expects," Sarkozy told a conference of new party members.
Sarkozy warned Friday that the demonstration was "taking on a new aspect" with the involvement of growing numbers of opportunist vandals.
Across the country police have made 1,420 arrests since the start of the trouble, and 453 people have been injured -- more than half of them police.
Two weeks of protests against the CPE and four days of national strikes have led to serious disturbances in two thirds of the country's universities and some 25 percent of the country's 4,370 high schools. Another day of national strikes has been planned by unions for Tuesday.
Opponents have said the law infringes on workers' rights, making it harder for young people to get long-term employment.
Opinion polls showed that some two thirds of the population want the CPE either modified or dropped.