BRUSSELS — 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 in November, authorities said 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 plus the suicide bombers died Tuesday in the blasts — two at the Brussels Airport departure terminal from homemade bombs hidden in luggage, and one at a subway station about 7 miles away in the heart of Brussels. The number of wounded climbed to 300 from 270 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 Wednesday 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.

Authorities recovered two undetonated bombs at the airport that had been constructed with between 20 and 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 a US 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 from 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 bomb 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 bombmaker, who has been linked to the Paris attacks.

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

The Belgian prosecutor said 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.

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

Areas such as the Brussels airport departure part of the terminal 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 such as Afghanistan and Iraq, and across the Middle East, bags are put through scanners when travelers enter the airport.

While Belgian authorities have been credited for 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,’’ Erdogan said at a news conference in Ankara.

Belgium’s justice minister, Koen Geens, acknowledged that Bakraoui had been deported to Europe last year, but he told the VRT broadcaster that he was not known to the Belgian authorities for terrorism, and was a common law 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 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 Van Leeuw. There, the prosecutor said, 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 8 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.

In claiming responsibility for the attacks, the Islamic State described a ‘‘secret cell of soldiers’’ dispatched to Brussels for the purpose. The shadowy cells were confirmed by the EU police agency, Europol, which said in a late January report that intelligence officials believed the group had ‘‘developed an external action command trained for special forces-style attacks.’’

The Associated Press, citing unidentified European and Iraqi intelligence officials, reported that the militant group has trained at least 400 fighters to target Europe in deadly waves of attacks. The officials said the group had a network of interlocking terror cells, according to the AP report.