A series of terrorist attacks in Brussels left 34 people dead and almost 200 injured on Tuesday, local media reported, with the Belgian capital under lockdown as authorities rushed to secure other sites and hunt down the perpetrators.

Two explosions that ripped through the departure hall at the Brussels airport around 8 am (0700 GMT) left 14 people dead and 81 people injured, the broadcaster VRT reported.

About an hour later - just as many commuters were headed to work - a second explosion went off in a subway train stopped at the station of Maelbeek, which is located near EU institutions. Twenty people died in that attack, while 106 were injured, according to VRT.

The federal prosecutor's office said in a statement that the three explosions "were terrorist attacks" and that a terrorism investigation has been launched.

The broadcaster RTBF reported that police raids were under way in the region of Brussels, adding that "people suspected of being linked to the attacks are actively sought."

Police operations were also still taking place at the airport on Tuesday afternoon, with investigators finding weapons and trying to determine if any other attackers may still be in the sprawling building, according to Belgian media.

The royal prosecutor called the airport blasts a suicide bombing.

The army's explosives team neutralized "a suspicious package" at the airport in the afternoon, the country's crisis centre wrote on Twitter, while police in the southern Brussels neighbourhood of Ixelles reported blowing up a "suspect" vehicle.

The airport, located about 15 kilometres from the Brussels centre, cancelled all flights after the attack.

Pictures posted on social media showed a blown-out window front, debris that appeared to come from a collapsed roof and bloodied people inside and outside the airport.

The airport explosions took place one after the other, the Belga news agency wrote, quoting eyewitnesses who said that they had heard shots and calls in Arabic beforehand.

Belgian authorities are working to secure "other sites" that are of concern, Prime Minister Charles Michel said, adding that military reinforcements have been deployed and controls are being carried out at Belgium's borders.

Evacuations were reported at universities and at the Tihange nuclear plant near the border with Germany, but the operator of the plant later said that it had only sent home "people who are not strictly necessary."

Belgium, the EU institutions and NATO all raised their threat alert levels after the attacks. In Belgium, it now stands at 4, indicating a "serious and imminent" threat.

The country had already been on high alert since the arrest in Brussels last week of Salah Abdeslam, a key suspect in the Paris terrorist attacks. Many of the perpetrators of those killings in November had links to the Belgian capital.

Michel called the latest attacks "blind, violent and cowardly."

"In this moment of tragedy, in this dark moment for our country, more than ever I want to call on everyone to display calm, but also solidarity. We are confronted with an ordeal, a difficult ordeal and we have to face this ordeal by being united," Michel said.

The European Commission, whose main building is less than 500 metres from the Maelbeek station, is continuing its work, spokesman Margaritis Schinas said.

"The European Union and the EU institutions must and will remain resolute. Here in the EU's capital, we stand together, united, against terror, in full solidarity with the people of Brussels," he said.

EU foreign policy chief Federica Mogherini broke down in tears at a press conference in Amman with Jordanian Foreign Minister Nasser Judeh, underlining the need for a message of "an Islam of peace and dialogue and cooperation."

The chief of the NATO military alliance, whose headquarters are about 5 kilometres away from the Brussels airport, said the killings were "an attack on our values and on our open societies."

"Terrorism will not defeat democracy and take away our freedoms," Secretary General Jens Stoltenberg said in a statement.

Some 1,600 additional security forces have been deployed to secure France's airports and train stations, Interior Minister Bernard Cazeneuve said.

"We are faced with a global threat," French President Francois Hollande said in Paris. "The war against terrorism must be conducted across Europe."

In Brussels, the entire public transport network was shut down Tuesday, while the city's tunnels were closed to car traffic. Train traffic to and from the Belgian capital was also disrupted.

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