CNN  — 

Paris attack suspect Salah Abdeslam is no longer cooperating with Belgian police and wants to be extradited to France as soon as possible, his lawyer, Sven Mary, said Thursday.

Investigators say they regard Abdeslam not only as a key figure in the November bombings and shootings that killed 130 people in Paris, but also as someone connected to the men who killed at least 31 in Tuesday’s bombings in Brussels, Belgium.

Belgian authorities captured Abdeslam after a shootout in Molenbeek, an impoverished suburb of Brussels last Friday – just four days before the Brussels attacks.

The Belgium-born French citizen was taken alive but wounded, authorities said.

French and Belgian officials had been looking at Abdeslam for months, believing he’d been in Paris on the night of the November 13 terror attacks there. Now he’s at least tangentially connected to the probe into Tuesday’s Brussels bombings, even though he was in custody at the time.

From Paris to Brussels

French investigators say they think Abdeslam was part of a team that attacked Paris with suicide bombings and shootings on November 13. His brother Ibrahim Abdeslam also was part of that group, killing himself in a bombing outside a cafe on Paris’ Boulevard Voltaire.

Authorities say Salah Abdeslam, 26, may have been the driver of a black Renault Clio that dropped off three suicide bombers near the Stade de France, one of the sites attacked in Paris.

They also think he’d worn a suicide belt that was found discarded on a Paris street after the attacks. Sweat on the belt matched Abdelslam’s DNA, a source close to the investigation told CNN.

Authorities say they believe he called friends to take him to Belgium after the attacks. He eluded investigators until March 15, when Belgian officials say they almost caught him in a raid on an apartment in the Forest district of Brussels.

Abdeslam was arrested three days later in Brussels, along with three members of a family accused of helping to hide him.

His lawyer, Mary, said over the weekend that Abdeslam was cooperating with investigators and fighting extradition to France.

Then came the attack in Brussels.

Brussels attack accelerated after arrest?

On Tuesday, with Abdeslam in jail, terrorists detonated bombs at Brussels’ airport and the city’s metro system. Besides those killed, about 300 people were injured.

Investigators suspect Abdeslam was probably going to be part of some type of attack involving the same people who ended up committing the Brussels bombings, a senior Belgian counterterrorism official told CNN.

Investigators believe the cell accelerated the Brussels plan when Belgian police raided the Forest apartment on March 15 and discovered that it had been Abdeslam’s hideout.

Who are the Brussels terror suspects?

One of the two brothers who ended up being suicide bombers in Brussels, Khalid and Ibrahim El Bakraoui, rented the Forest apartment, definitively connecting the Paris and Brussels attack cells, the official said.

The Belgian federal prosecutor revealed Wednesday that Ibrahim El Bakraoui left behind a will found in a laptop computer near a bomb factory raided Tuesday in the city’s Schaerbeek district. In the documents, Bakraoui stated he “needs to rush” and “no longer feels safe.” He also said that if he takes too much time, he would end up “next to him in prison” – an apparent reference to Abdeslam the Belgian investigators believe, the official told CNN.

Abdeslam’s next hearings in Belgium are scheduled for March 31 and April 7, his lawyer said.

How world reacted to Brussels bombings

CNN’s Paul Cruickshank contributed to this report.