By Caroline Wyatt
BBC News, Paris
French PM Dominique de Villepin has indicated he is willing to be flexible on at least one key element of a controversial youth employment law.
Students say they will continue protests
He said he is willing to cut the length of a trial period from two years.
However, he said he would not withdraw the contract entirely, as trade unions and students have demanded in a battle of strength with the government.
French students plan more protests for Thursday, while trade unions are planning a day of action next Tuesday.
The prime minister told the National Assembly on Wednesday that he understood the feelings of young people in France and wanted talks to help resolve the issue.
"Anxieties are being expressed. I understand what the young people in our country are feeling and saying. I understand their wish to take their place in our society, their wish to be listened to, their wish to be heard," he said.
"I would like to move forward with the employers and trade unions without preconceptions, to begin together all the necessary discussions."
'Room for manoeuvre'
French students say they are determined to fight on until they force the government to back down.
This battle of wills is once again destabilising France, which could erupt into widespread violence, as it did in the poorer city suburbs last November
On Tuesday, some 5,000 students marched across the Left Bank in Paris, chanting: "The street rules".
But Mr de Villepin is determined to prove that it does not.
He insists that his government will not give in to trade unions or students who want him to rescind the new law.
Mr de Villepin has indicated there is some room for manoeuvre - for example, that the trial period during which employers could sack young people could be reduced to under two years.
But that is not enough for French trade unions, who say they will call out as many sectors as possible on strike next Tuesday.
All this is putting severe pressure on the prime minister, who is seeing unity in his ranks crumble on the issue.
With polls showing that 70% of the French are against the new law, many of his own MPs are advising him to back down.
De Villepin faces pressure from protesters and his own party
The left in France is also whipping up anger by focusing attention on a protester left in a coma after Saturday night's violent clashes at Place de la Nation in Paris.
Some claim he was trampled by riot police, although the police trade union says he was struck by rioters.
This battle of wills is once again destabilising France, which could erupt into widespread violence, as it did in the poorer city suburbs last November.
It is all part of a much wider fight over how France adapts to face the challenges of globalisation and whether it can keep the jobs-for-life culture that so many here cherish, even though it has led to widespread unemployment, especially among the young.