By Alastair Macdonald, Ingrid Melander and Foo Yun Chee

BRUSSELS (Reuters) - Belgian police arrested six people in their probe of Tuesday's Islamic State suicide bombings in Brussels, while authorities in France said they thwarted a militant plot there "that was at an advanced stage."

The federal prosecutor's office in Belgium said on Thursday that the arrests came during police searches in the Brussels neighborhoods of Schaerbeek in the north and Jette in the west, as well as in the center of the Belgian capital.

The arrests came days after suicide bombers hit the Brussels airport and a metro train, killing at least 31 people and wounding some 270 in the worst such attack in Belgian history.

The attack in Brussels, which is home to the European Union and NATO, has heightened security concerns around the world and raised questions about European countries' response to the threat from Islamist extremists.

The Islamic State militant group, which claimed responsibility for the Brussels bombings, also took credit for coordinated attacks in Paris in November that killed 130 people at cafes, a sports stadium and concert hall.

In Paris on Thursday, authorities arrested a French national suspected of belonging to a militant network planning an attack in France.

French Interior Minister Bernard Cazeneuve said in a televised address that the arrest helped "foil a plot in France that was at an advanced stage."

Cazeneuve added that the man arrested "is suspected of high-level involvement in this plan. He was part of a terrorist network that planned to strike France."

After the arrest by the French counterterrorism service, DGSI, the agency raided an apartment building on Thursday night in the northern Paris suburb of Argenteuil. French TV station ITele reported that explosives had been found in the man's house.

"At this stage, there is no tangible evidence that links this plot to the attacks in Paris and Brussels," added Cazeneuve, who was in the Belgian capital earlier on Thursday.

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RESIGNATION OFFERS

Earlier on Thursday, Belgium's interior and justice ministers offered to resign over a failure to track an Islamic State militant expelled by Turkey as a suspected fighter and who blew himself up at Brussels Airport.

Brahim El Bakraoui was one of three identified suspected suicide bombers who hit the airport and metro train. At least one other man seen with them on airport security cameras is on the run and a fifth suspected bomber filmed in the metro attack may be dead or alive.

Bakraoui's brother Khalid, 26, killed about 20 people at Maelbeek metro station in the city center. De Morgen newspaper said he had violated the terms of his parole in May by maintaining contacts with past criminal associates, but a Belgian magistrate had released him.

Interior Minister Jan Jambon and Justice Minister Koen Geens tendered their resignations to Prime Minister Charles Michel, who asked them to stay on. "In time of war, you cannot leave the field," said Jambon, a right-wing Flemish nationalist.

Turkish President Tayyip Erdogan said Bakraoui, 29, had been expelled in July after being arrested near the Syrian border and two officials said he had been deported a second time. Belgian and Dutch authorities had been notified of Turkish suspicions that he was a foreign fighter trying to reach Syria.

At the time, Belgian authorities replied that Bakraoui, who had skipped parole after serving less than half of a nine-year sentence for armed robbery, was a criminal but not a militant.

"You can ask how it came about that someone was let out so early and that we missed the chance to seize him when he was in Turkey. I understand the questions," Jambon said. "In the circumstances, it was right to take political responsibility and I offered my resignation to the prime minister."

Geens said systems should be reviewed but noted that other countries had been attacked, citing the Sept. 11, 2001, attacks on the United States in which he noted that "there were 3,000 dead."

JIHADIST NETWORK

Investigators are convinced the same jihadist network was involved in the November Paris attacks.

Belgian public broadcaster VRT said investigators believed that Paris attacks suspect Salah Abdeslam, arrested last Friday, probably planned a similar shooting and suicide bomb attack in Brussels.

One man was killed in a shootout with police on March 15 that led to the discovery of assault weapons and explosives and the arrest of Abdeslam, 26, and another suspect on March 18.

Belgium lowered its security alert level one notch to three from the highest level, four, but officials did not say what that would mean in terms of security measures that have included a heavy police and military presence in Brussels.

Islamic State posted a video on social media calling the Brussels blasts a victory and featuring the training of Belgian militants suspected in the Paris attacks.

The lawyer for Abdeslam said the French national wanted to "explain himself" and would no longer resist extradition to France. His lawyer, Sven Mary, said Abdeslam had not been aware of the plan for the Brussels airport and metro attack that was carried out by men who had shared hideouts with him.

Two sources familiar with the matter said the Bakraoui brothers had been on U.S. government counterterrorism watch lists before the attacks. But it was not clear how long they had been known to the authorities.

'A NICE BOY'

Security sources told Belgian media the other suicide bomber at the airport was Najim Laachraoui, a veteran Belgian Islamist fighter in Syria suspected of making explosive belts for November's Paris attacks.

Laachraoui's younger brother Mourad issued a statement condemning his actions, in the first public reaction from a family member of one of the Brussels attackers.

Laachraoui, 25, gave no warning sign of being radicalised before leaving for Syria in 2013 and breaking all contact with his family, Mourad told a news conference.

"He was a nice boy, and above all he was clever, that's what I remember of him," Mourad said of his brother, who graduated in electromechanics. He said the last time he saw him, he looked "normal."

(Additional reporting by Miriam Rivet, Geert De Clercq and John Irish in Paris, and Philip Blenkinsop, Julia Fioretti, Barbara Lewis, Bate Felix, Jan Strupczewski, Robin Emmott and Jean-Baptiste Vey in Brussels; Writing by Peter Cooney; Editing by Cynthia Osterman)