"We have a not a bad amount of pieces of the puzzle and in the last few days several pieces have found their place. But I am still, and we are still, far from solving the puzzle," Frederic Van Leeuw told a news conference.
"We hope to go as far as possible," he said.
Van Leeuw added that Abdeslam "was heard" by investigators following his capture in a police raid in Brussels on Friday "but then again he was not in good form as you can imagine because he was wounded."
Paris prosecutor Francois Molins said that France expected Abdeslam's extradition over the November 13 gun and suicide bomb attacks in which 130 people were killed.
"There is a strong expectation from the French justice authorities and particularly from the families of the victims that Salah Abdeslam comes to explain himself," Molins said.
"It's up to Salah Abdeslam to decide -- either he agrees and can be transferred rapidly, or he doesn't consent and it will be up to the Belgian authorities to decide whether there is any reason that could allow the refusal of his transfer."
Investigators have traced Abdeslam's travels in the months before the attacks to Germany, Austria and Hungary.
He fled to Brussels after the attacks, passing through three French police checks, but apart from three weeks when he was believed to be in a flat in the north of the capital, his whereabouts during the past four months are unknown.
"We don't have the full timeline for what Salah Abdeslam did between November 14 and his arrest," Van Leeuw said.
"I have no concerns on that point," he said, adding that he was working on a "joint file" with Belgian authorities and "with joint dossiers we are allowed to express ourselves.
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