Local media said authorities had followed a tip from a taxi driver who believed he may have driven the bombers to the airport.
Investigators said they were focusing on a man in a hat who was caught on CCTV pushing a laden baggage trolley at the airport with two others they believed were the bombers. An unused explosive device was later found at the airport and a man was seen running away from the terminal after the explosions.
Security experts believed the blasts, which killed about 20 on a metro train running through the area that houses European Union institutions, were probably in preparation before March 18's arrest of locally based French national Salah Abdeslam, 26, whom prosecutors accuse of a key role in the November 13 Paris attacks.
He was caught and has been speaking to investigators after a shootout at an apartment in the south of the city a week ago, after which another Islamic State flag and explosives were found. It was unclear whether he had knowledge of the new attack or whether accomplices may have feared police were closing in.
Islamic State said in a statement that "caliphate soldiers, strapped with suicide vests and carrying explosive devices and machineguns" struck Zaventem airport and Maelbeek metro station.