"Salah Abdeslam has asked me to inform you that he wishes to leave for France as quickly as possible", Mary said, adding that he "wants to explain himself in France".
Belgian authorities on Wednesday said one of the men who carried out the terrorist bombings in Belgium this week was also heavily involved in the bloody coordinated attacks in Paris four months ago.
Belgian Federal Prosecutor Frederic Van Leeuw identified two of the Brussels attackers as brothers - Ibrahim El Bakraoui, a suicide bomber at the airport, and Khalid El Bakraoui, who targeted the subway.
Belgian authorities searched Wednesday for a man pictured at the Brussels airport with two apparent suicide bombers, amid growing suggestions that the bombings of the Brussels airport and subway were the work of the same Islamic State cell that attacked Paris past year.
Belgium will observe three days of national mourning.
Twin terror raids in France and Belgium Thursday resulted in multiple arrests, including one Frenchman who was described as being in the "advanced stages" of a plot to attack the country.
Abdeslam, 26, who was shot in the leg during his arrest last Friday in the Brussels suburb of Molenbeek, "is recovering bit by bit from his injury, which was not serious", Mary said.
In February, Belgian Interior Minister Jan Jambon said that there was only a threat "to the person in question, but not the nuclear facilities".
Experts believe that the attackers had planned to blackmail the nuclear official in order to make a "dirty bomb", - an improvised nuclear device that could spread radioactive material across a wide area, reports NBC News.
The AP reports that officials estimate between 400 and 600 Islamic State fighters trained specifically for external attacks, and that some 5,000 Europeans have gone to Syria.
Two officials told The Associated Press that Laachraoui's DNA was verified as that of one of the suicide bombers Tuesday, after samples were taken from remains found at the blast site at Brussels airport.
French prosecutors have said that the bombs used in the November Paris attacks were made from triacetone triperoxide, or TATP.
There has been some speculation that the "man in white" was a handler or supporter for Laachraoui and El-Bakraoui since he was not wearing a glove on his left hand like they were, which may have been hiding a trigger, and his bomb failed to detonate until after it was secured by law enforcement.
Turkey has previously complained that Western countries did not heed warnings of the dangers posed by jihadists it had expelled back to Europe after arresting them on the Syrian border.
One of those suicide bombers has already been identified as the second El Bakroui brother, Khalid. Those attacks killed 130 people.
Brussels airport is to remain closed until at least Saturday, the airport announced, saying forensic investigation by police was still underway and they had not yet had time to assess the damage.
Candles, Belgian flags and teddy bears were piling up in the central Place de la Bourse with tributes left to the innocent victims of the attacks.
European security authorities faced mounting pressure after it emerged that two brothers who blew themselves up at the airport and on a metro train were known to police and that one of them had been deported from Turkey as a "foreign terrorist fighter".