UN chief Ban Ki-moon said those responsible for the
"despicable" bombings should face justice, while Belgian King Philippe condemned the "cowardly and odious" attacks.
Hundreds of flights and trains were cancelled as Europe tightened security, while the US warned citizens about the "potential risks" of travelling in Europe and New York and Washington stepped up security.
There were chaotic scenes at Brussels airport after the bombers struck around at around 8:00 am (1230 IST), as plumes of dark smoke could be seen rising from holes punched through the roof of the building by the blasts.
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About an hour after the airport blasts, a third explosion rocked Maalbeek metro station, in the heart of the city's EU quarter, just as commuters were making their way to work.
Paramedics tended to commuters with bloodied faces as the city's normally peaceful streets filled with the wailing of sirens.
Pierre Meys, spokesman for the Brussels fire brigade, told AFP at least 14 people had been killed at the airport, while Brussels mayor Yvan Mayeur said "around 20" died in the metro.
More than 200 people were wounded in the two attacks, including four Mormon missionaries -- three Americans and one French -- two Britons, two Colombians and an Ecuadoran. France said eight of its nationals were hurt, though it was unclear if this included the Mormon.
Belgian authorities published surveillance images showing the three male suspects of the airport attack. Two had dark hair and were wearing a glove on only one hand, and a third, who is being hunted by Belgian police, was wearing a hat and a white coat.
"They put their suitcases on trolleys, the first two bombs exploded. The third also put his on a trolley but he must have panicked, it didn't explode."
Belgian authorities had been on alert after Abdeslam, Europe's most wanted man, told investigators he had been planning an attack on Brussels.
Last Tuesday an Algerian IS-linked militant was killed in a shoot-out in the south of the city.
Investigators believe Abdeslam slipped out of the apartment as the gun battle erupted. He was arrested three days later in Brussels' gritty Molenbeek district, just around the corner from his family home.