Belgian state broadcaster RTBF has identified two of the attackers who targeted Brussels as brothers Khalid and Brahim Bakraoui.
The report issued today says the brothers were known to police for past crimes, but nothing relating to terrorism.
REBF says Khalid El Bakraoui had rented an apartment raided by police last week in an operation that led authorities to top Paris attacks suspect Salah Abdeslam.
World leaders united in condemning the carnage in Brussels and vowed to combat terrorism, after Islamic State bombers killed around 35 people in a strike at the symbolic heart of the EU.
Global landmarks from the Eiffel Tower in Paris to Berlin's Brandenburg Gate were lit up in the black, yellow and red of the Belgian national flag in solidarity.
In Brussels, hundreds crowded into Place de la Bourse in the capital's historic centre to grieve for the dead, while in London fans of Adele lit up the O2 stadium with their phones after the pop star asked them to "take a moment for Brussels".
The European Union vowed to defend democracy and combat terrorism "with all necessary means" after the bombings at Brussels airport and a metro station, only a short walk from the bloc's core institutions.
The EU said the Brussels attacks were an assault "on our open democratic society" at a time when the bloc is already on edge after a wave of jihadist violence.
"This latest attack only strengthens our resolve to defend the European values and tolerance from the attacks of the intolerant. We will be united and firm in the fight against hatred, violent extremism and terrorism," leaders and its institutions said in a statement.
Officials said around 20 people were killed on the metro and 14 at the airport in the rush-hour assaults, which came days after the main fugitive suspect in November's gun and bomb rampage in Paris was arrested in Brussels.
"Our Union's capital is under attack. We mourn the dead and pledge to conquer terror through democracy," the Greek foreign ministry said on Twitter. "Nous sommes tous Bruxellois" -- "We are all citizens of Brussels."
Belgian colours lit up the Eiffel Tower in Paris, and hundreds joined a vigil in support of the Brussels victims. Flags were to fly at half mast in France, a nation still raw from last year's jihadist rampage.
"The whole of Europe has been hit," French President Francois Hollande declared, urging the continent to take "vital steps in the face of the seriousness of the threat".
German Chancellor Angela Merkel vowed that "the horror is as boundless as the determination to defeat terrorism" and British Prime Minister David Cameron vowed: "We will never let these terrorists win."
US President Barack Obama branded the attacks "outrageous", calling on the world to stand "together
regardless of nationality or race or faith in fighting against the scourge of terrorism".
"We can and we will defeat those who threaten the safety and security of people all around the world," he said in Havana.