BRUSSELS, March 23 — The Brussels suicide bombers included two Belgium-born brothers with a violent criminal past and suspected links to plotters of the Islamic State’s Paris attacks last November, the authorities said on Wednesday, raising new alarms about Europe’s leaky defenses against a militant organization that has terrorized two European capitals with seeming impunity.

One of the brothers was deported by Turkey back to Europe less than a year ago, Turkey’s president said, suspected of being a terrorist fighter intent on entering Syria, where the Islamic State is based. Despite that statement, Belgian officials said neither brother had been under suspicion for terrorism until recently, an indication of the Islamic State’s ability to remain steps ahead of European intelligence and security monitors.

At least 31 people as well as the suicide bombers died on Tuesday in the blasts — two at the Brussels international airport departure terminal from homemade bombs hidden in luggage, and one at a subway station about seven miles away in the heart of Brussels. The number of wounded climbed to 300 from 270 on Wednesday as the area slowly sought to recover from one of the deadliest peacetime assaults in Belgium’s history.

“The European values of democracy and of freedom are what was savagely assaulted by these tragic attacks,” Prime Minister Charles Michel said after meeting with his French counterpart, Manuel Valls, who said, “Our two peoples are united in this hardship.”

Many Belgians attended memorials and others stayed home from work. Subway service was reduced and the airport, now a crime scene, was to remain closed at least through Thursday. And new evidence emerged of how the magnitude of the attacks could have been far worse.

The authorities recovered two undetonated bombs at the airport that had been constructed with 20 to 40 pounds of a volatile compound known as TATP — an explosive also used in the Paris attacks — combined with ammonium nitrate and metal bolts and nails, according to an American official who had reviewed intelligence shared by Belgium. The official said they also recovered what the Belgians called a suicide belt at the site, and found two more bombs concealed in suitcases, similar to those recovered at the airport, at the residence where the bombers hailed a taxi before Tuesday morning’s attacks.

As of Wednesday evening, the police were still hunting for at least one other member of the Brussels bombing ring, a man in a white coat and dark hat seen pushing a luggage cart in an airport surveillance photo, who was believed to have escaped before the explosions. They were also trying to determine if the other suicide bomber at the airport was Najim Laachraoui, 24, a Belgian believed to be a bomb maker, who has been linked to the Paris attacks.

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There were indications that the Brussels bombers may have acted out of urgency because they feared discovery after the arrest on Friday in Belgium of the only remaining survivor among the Paris attackers, Salah Abdeslam, who is said to be cooperating with the authorities.

The Belgian prosecutor said the authorities found a recently composed will — which was possibly a suicide note — of the elder brother involved in the Brussels bombing, Ibrahim el-Bakraoui, 29, on a discarded computer in a garbage can. The will expressed his fear of being caught and ending up in a prison cell.

Mr. Bakraoui and the unidentified bomber blew themselves up at the Brussels airport at 7:58 a.m. Tuesday, in two explosions nine seconds apart. At 9:11 a.m., his younger brother, Khalid el-Bakraoui, 27, carried out the suicide attack at the Maelbeek subway station.

While the Belgian authorities have been credited with acting quickly in the aftermath of the assaults, there were growing questions about whether they had also suffered an enormous intelligence lapse.

The most prominent question arose from assertions by Turkey’s president, Recep Tayyip Erdogan, that his government had detained Ibrahim el-Bakraoui near the Syrian border on June 14, alerted the Belgian government that he “was a foreign terrorist fighter,” and then deported him to the Netherlands.

“Despite our warnings that this person was a foreign terrorist fighter, the Belgian authorities could not identify a link to terrorism,” Mr. Erdogan said at a news conference in Ankara.

Justice Minister Koen Geens of Belgium acknowledged that Mr. Bakraoui had been deported to Europe last year, but he told the VRT broadcasting service that he was not known to the Belgian authorities for terrorism but was a common criminal who had been given conditional release from prison.

In his own news conference, Frédéric Van Leeuw, the Belgian federal prosecutor, described the trail that led investigators to identify the brothers.

After the attacks, a taxi driver who suspected that he may have driven the bombers to the airport approached the police and led them to a house on Rue Max Roos, in the Schaerbeek neighborhood of Brussels, where he said he had picked up three men, according to Mr. Van Leeuw. There, the prosecutor said, the authorities found about 33 pounds of TATP, considered a large amount.

At the apartment in Schaerbeek, investigators also found nearly 40 gallons of acetone and nearly eight gallons of hydrogen peroxide. Acetone, a solvent in nail polish remover, and hydrogen peroxide, found in hair bleach, are among the ingredients used to make TATP. The investigators also found detonators, a suitcase full of nails and screws, and other materials that could be used to make explosive devices.

On Wednesday, the Belgian police raided a building in the Anderlecht neighborhood of Brussels. Officers in protective clothing carted out files and plastic boxes as masked officers stood guard outside. Two police officers in the neighborhood said an arrest had been made, but the identity of that person was not clear.

Several Belgian news outlets reported last week that the Bakraoui brothers, who grew up in the working-class Laeken neighborhood, were wanted for questioning in connection with a March 15 raid on an apartment in the Brussels suburb of Forest, which had been linked to the Paris attacks. It was not clear why the authorities did not formally ask the public to help find them.

Ibrahim el-Bakraoui was sentenced in 2010 to nine years in prison for shooting at police officers after a robbery attempt at a currency exchange office. It was not clear when or why he was released, or how he ended up in Turkey.

In 2011, Khalid el-Bakraoui was sentenced to five years in prison for attempted carjacking; when arrested, he was in possession of assault rifles. Interpol issued a warrant for him in August after he violated his parole. He is believed to have used a false name to rent a safe house in Charleroi, Belgium, and the apartment in Forest. Fingerprints belonging to two of the Paris attackers, Abdelhamid Abaaoud and Bilal Hadfi, were found in the Charleroi house on Dec. 9, and Mr. Abdeslam’s prints were found in the Forest apartment.

Speaking on Belgian radio on Wednesday morning, Interior Minister Jan Jambon said that the police raids would continue, and that the threat status would remain at its highest, Level, 4. “There are many hypotheses to put on the table,” he said. “It’s up to investigators to sort out fact from fiction.”

Speaking later to RTL radio, Mr. Jambon said it was also unlikely that the attacks could have been avoided even if Belgium had been at the highest threat level instead of Level 3, which was imposed after the Paris attacks.

He said Belgium had “everything possible in place to avoid a catastrophe like what happened yesterday, like other countries.”

Areas like the Brussels airport departure hall are particularly vulnerable because, as at most Western airports, bags are not searched until after check-in. That allows a would-be attacker to pack a bomb into a suitcase that could have far more space than an explosive vest and therefore be far more lethal.

In terrorism-plagued countries like Afghanistan and Iraq, and across the Middle East, bags are put through scanners when travelers enter the airport.