Employers' groups also met Dominique de Villepin on Friday to tell him the contract might not be the best way to reduce unemployment and warn him the violence was endangering the economy.
Villepin said the 90 minutes of union talks, in the run-up to a national strike on Tuesday, were "an important first step" and he hoped for more discussions in the coming days.
But he made it clear he would not heed their call to abandon the CPE First Job Contract.
Jacques Chirac, the president, who has pushed his prime minister to renew the dialogue with unions, said Villepin was ready to take account of protesters' views but condemned rioting by youths which marred demonstrations in Paris and some provincial cities.
In a short statement after the union meeting, Villepin told reporters: "This meeting with the trade unions was important. It was a first step.
"Together, we have to succeed in finding constructive solutions to respond to young people's real worries, especially on the CPE."
Disappointed union chiefs said they had failed to get Villepin to scrap the CPE, which allows employers to fire employees under 26 without stating a reason within their first two years in a job.
Bernard Thibault of the leading CGT union said: "We tried to persuade him, one after another, of the scale of the crisis, and that there was no other possible response but to withdraw it."
Union leaders said no further meetings with the government were yet planned.
Protesters want the new youth
jobs law scrapped altogether
Villepin said he hoped the parties would meet again next week and would host student leaders on Saturday.
He says the contract will encourage businesses to hire the young and help to bring down youth unemployment of 23%.
Some employers say it is not the best way to create jobs.
Pierre Perrin, president of the UPA group of artisans, said after the meeting: "For us, singling out the CPE as the only tool against unemployment is not the solution."
Business group Medef warned Villepin that the economy could suffer from the protests and the violence linked to them.
Laurence Parisot, Medef president, said: "We think they are endangering the economy of our country, that they are endangering the image and the reputation of our country and the strength of our social fabric."
Friday's meetings came a day after rampaging youths torched cars, looted shops and robbed student demonstrators at the end of student protest marches in Paris and major provincial cities.
In all, 630 people were arrested and 90 officers were injured in the clashes, police said.
In Paris, riot police fired tear gas as they moved to quell violence that left one student in hospital with a serious head injury.
Rampaging youths have torched
cars and looted shops
Speaking after a summit of EU leaders in Brussels, Chirac said rioters should be firmly punished and said the government could not bend to pressure from the street.
"There is no question of an ultimatum. When a law has been adopted, it must be applied," he told a news conference.
Thursday's disturbances brought into the heart of Paris scenes reminiscent of last autumn's riots in poor suburbs.
Youths battled police and smashed car windows with the Eiffel tower as a backdrop, watched by startled tourists.
Nicolas Sarkozy, the interior minister, ordered police to intervene promptly when violence erupted, after criticism they had reacted too slowly to Thursday's incidents.
On Friday youths smashed up a research centre in southern Paris after occupying it for three days as a protest against the CPE.
The protests have split the governing conservatives and affected Villepin's popularity, hurting his chances of running in 2007 elections should Chirac, as expected, not run for a third term.
Villepin needs the measure to win support with conservative voters to boost his presidential credentials, while Sarkozy, his chief rival on the right, has distanced himself from the measure and called for it to be given a six-month trial.