Salah Abdeslam, a suspect in last year's Paris attacks who was arrested in Belgium last week, is "worth his weight in gold" to investigators, his lawyer has said.
"He is collaborating... He is not maintaining his right to remain silent," said lawyer Sven Mary.
Abdeslam was captured in a raid on an apartment in Brussels and is being interrogated by police.
He is the only surviving participant in the attacks in police custody.
However, Mr Mary denied media reports that Abdeslam, 26, would become an informer in return for more lenient treatment.
Abdeslam, a Belgian-born French national dubbed Europe's most-wanted fugitive, is now fighting extradition to France.
In other developments:
- French President Francois Hollande has met relatives of some of the 130 people killed in the 13 November attacks
- Belgium's federal prosecutor said the authorities had made progress but were "still far from solving the puzzle" of the Paris attacks
- Belgian prosecutors say that DNA evidence had identified one of Abdeslam's accomplices as Najim Laachraoui, 24, who is still on the run.
Abdeslam's lawyer has previously threatened to sue French investigator Francois Molins for telling journalists that Abdeslam had wanted to blow himself up along with other attackers but he changed his mind.
Mr Mary said this was a violation of judicial confidentiality. Mr Molins said he had the right to reveal the investigation's progress in an "objective" manner.
Mr Mary also said his client would continue to fight a transfer to France, but added: "Let's be quite clear. He's going to France. It'll be the investigating judge who decides when he goes."
French president Francois Hollande has said that the number of people involved in the terrorist network is much larger than originally thought and that he wants Abdeslam transferred to France as soon as possible to face prosecution.
Belgian prosecutors said that Abdeslam had travelled twice to the Hungarian capital Budapest, using a rental car last September.
In the car were two other men, using fake Belgian identity cards with the names Samir Bouzid and Soufiane Kayal.
Soufiane Kayal has now been identified as Laachraoui from DNA found at houses in the town of Auvelais and the Brussels district of Schaerbeek.
"The investigation showed that Soufiane Kayal can be identified as Najim Laachraoui, born on 18 May 1991 and who travelled to Syria in February 2013," the statement said.
Belgian police said Samir Bouzid was "most probably" Mohamed Belkaid. He was killed by a police sniper in a raid on a flat outside Brussels on 15 March.
The prosecutor appealed for public help in finding Laachraoui.
Also still being sought is Mohamed Abrini, who was filmed at petrol stations with Abdeslam two days before the Paris attacks.
The BBC's Lucy Williamson in Paris says that for those who lost relatives in the attacks, relief at Abdeslam's arrest is quickly turning to hunger for the information he might provide.
"We hope [his arrest] will help us in the search for truth," read the message from one support group set up after the November attacks.
But our correspondent says Mr Hollande's first formal meeting with relatives comes amid recrimination that they were ignored for four months.
Those who met Mr Hollande at the Elysee palace called for better support from the state.
After the meeting, Emmanuel Domenach, who survived the Bataclan attack said "we felt we were heard, even if there was no concrete progress".
France has tightened security at its borders after Abdeslam's arrest.
Belgian Foreign Minister Didier Reynders has suggested that the suspect was preparing attacks in Brussels before he was apprehended.
The Belgian authorities have charged Abdeslam with terrorism offences.
Another man arrested at the same time as Salah Abdeslam, Monir Ahmed Alaaj, has also been charged with participation in terrorist murder and the activities of a terrorist group, Belgian prosecutors say.