Belgian media have published a security camera picture of three men they said police suspected of carrying out the bombings.
The still photograph shows young three men with dark hair, pushing laden luggage trolleys. Their identities were unknown.
Belgian federal prosecutors had asked media earlier on Tuesday not to release the picture for the good of the investigation, but it leaked on social media, the VTM broadcaster said.
A witness said he heard shouts in Arabic and shots shortly before two blasts struck a packed airport departure lounge at Brussels airport.
US President Barack Obama led calls of support to Belgian Prime Minister Charles Michel after Brussels went into a state of virtual lockdown.
"We must be together regardless of nationality or race or faith in fighting against the scourge of terrorism," Obama told a news conference in Cuba.
"We can and we will defeat those who threaten the safety and security of people all around the world."
Michel spoke at a Brussels news conference of a "black moment" for his country. "What we had feared has come to pass."
Australian Prime Minister Malcolm Turnbull tweeted that Australians' "thoughts, prayers & solidarity are with the people of Belgium".
Foreign Minister Julie Bishop condemned the attacks and said the Department of Foreign Affairs and Trade was urgently seeking to determine whether any Australians had been caught up in them.
"We have upgraded our travel advice for Belgium to advise Australian travellers to reconsider their need to travel," she said in a statement.
The blasts appeared to be linked to the arrest in a Brussels shoot-out four days ago of French citizen Salah Abdeslam, a suspected participant in the November 13 militant attacks in Paris that killed 130 people.
All public transport in Brussels was shut down after Tuesday's attack, people were urged to stay indoors and extra troops were sent into the city.
Later, people were told that mainline rail stations would open at 4pm (local time) to let commuters head home.
Public broadcaster VRT said police had found a Kalashnikov assault rifle next to the body of an attacker at the airport and an unused explosive belt was also found.
Alphonse Youla, 40, who works at the airport, told Reuters he heard a man shouting out in Arabic before the first explosion. "Then the glass ceiling of the airport collapsed."
"I helped carry out five people dead, their legs destroyed," he said, his hands covered in blood.
Video showed devastation in the departure hall with ceiling tiles and glass scattered across the floor.
A Crisis Centre spokesman issued provisional figures of 20 killed in the metro and ten at the airport. Public broadcaster VRT had said earlier 20 were killed in the train and 14 at the airport.
Britain, Germany, France and the Netherlands, all wary of spillover from conflict in Syria, were among states announcing extra security measures.
Brussels airport said it had cancelled all flights until at least 6am on Wednesday.
All three main long-distance rail stations in Brussels were closed and train services on the cross-channel tunnel from London to Brussels were suspended.