"They came in a taxi with their suitcases, their bombs were in their bags," Zaventem mayor Francis Vermeiren told AFP.
"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," he added.
It was this case that bomb disposal experts blew up later, he added.
Vermeiren said of the airport attacks that "it was a war zone, atrocious to see, atrocious to live through. But strength and solidarity have won."
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Police issued a wanted notice for the suspect, along with a CCTV picture showing a bespectacled man with a goatee beard, wearing a white jacket and black hat, pushing a trolley with a large black bag.
Authorities earlier released a grainy picture of the same man alongside two men with dark hair in dark clothes who were also pushing trollies with similar bags.
Both of those men wore black gloves on their left hands.