The city is on lockdown amid fears of further terror bombs
Islamic State has claimed it carried out the deadly attacks on Brussels.
The militant group claimed responsibility for the two attacks in a statement released on its official account with the social media site Telegram.
It said: "We promise the crusader alliance against the Islamic State that they will have black days in return for their aggression against the Islamic State."
Belgium is one of dozens of countries which have met to discuss tackling the group, which has taken large swathes of territory in Syria and Iraq.
Earlier, the AMAQ news agency, which is affiliated to the jihadist organisation, said: "Islamic State fighters opened fire inside Zaventem Airport, before several of them detonated their explosive belts, as a martyrdom bomber detonated his explosive belt in the Maalbeek metro station."
At least 34 people have been killed in two attacks on the Belgian capital's Zaventem Airport and metro system.
The blasts came four days after the arrest of Salah Abdeslam, who authorities believe took part in November's attacks on Paris, which were also claimed by IS.
Shots were fired as the attackers at the airport reportedly shouted in Arabic before two explosions.
About 70 minutes later, Maalbeek metro station near the EU offices was targeted in a separate attack during the morning rush hour.
Police released a photo showing three men who could be involved in the bombings, pushing trolleys, and said that one of them is on the run.
A CCTV image of the suspect has been released by Belgian police:
The government has condemned the attacks in Brussels as "deplorable", and that "there can never be any justification for such brutality".
A meeting has been held of the National Security Council - which includes the Garda Commissioner, the Chief of Staff of the Defence Forces and the heads of four government departments.
Following the meeting, a statement was issued: "Our thoughts are with the families and friends of all those who have lost their lives, and also with the injured and we hope for their speedy recovery".
"While it remains the case that there is no specific information in relation to any threat to Ireland from international terrorism we cannot consider that we are immune from the threat".
"It remains the case that an attack here is assessed as possible but not likely".
The statement adds: "The activities of a small number of people based here and whose behaviour may be of concern will continue to be monitored closely".
Public transport was suspended and people were told to stay in their homes and offices as the Belgian capital was put on lockdown amid fears of further attacks.
Three days of national mourning have been declared in Belgium.
The country's federal prosecutor said all three explosions were terrorist attacks.
"There were two explosions in the departure area, one probably caused by a suicide bomber," said Frederic Van Leeuw of the attack on the airport.
Two people were arrested by armed police at the city's Noord railway station as officials said they feared "people are still at large".
Multiple reports suggest anti-terror raids are now under way in Schaerbeek, north-east of central Brussels, according to Belgian police sources.
Some of the 96 people injured in the airport blasts suffered fractures and deep cuts caused by flying glass and nails, suggesting the bombs had been packed to cause maximum damage.
There was a controlled explosion of a suspect package at the Vrije University in central Brussels - as the country's Tihange nuclear power plant was evacuated.
John Harkin is from Co Sligo, but works at CEEMET in Brussels. He spoke to Newstalk Lunchtime.
As the city went into lockdown, Belgian Prime Minister Charles Michel condemned the "violent" attacks as "cowardly" on what he described as "a black day" for the nation.
"What we feared has happened, we were hit by blind attacks," he said.
"This is a dark moment for our nation. We need calm and solidarity".
He says the investigation into who was responsible is continuing.
The French President, Francois Hollande, says the war against terrorism is now being fought by all of Europe.
Brussels Airport itself has released a statement, expressing its deepest sympathy with the victims and relatives, and thanking those who helped.
"On behalf of the entire airport community, I would like to extend our warmest condolences to the family and friends of the victims of these cowardly and heinous acts", Brussels Airport CEO Arnaud Feist said.
"I would like to extend a heartfelt thank you to the emergency and rescue services, passengers and staff for their compassion, solidarity and help. This is without doubt the blackest day in the history of Brussels Airport".
All flights and other operations at Brussels Airport have been cancelled for the day. The airport site has been entirely evacuated to give the public prosecutor and the police time to carry out their investigation.
"Brussels Airport is fully collaborating with the judicial and police services. Forensic investigation by the public prosecutor and the police in the terminal is still underway", the statement adds.
"Until the investigation is complete, nobody is allowed to enter the departures hall, including the airport staff".
The attacks follow the dramatic arrest of Paris attacks suspect Salah Abdeslam in the Belgian capital on Friday - four months after November's terror in the French capital that left 130 people dead.
Authorities have said it is unclear if he is linked to Tuesday's suspected coordinated attacks.
Some 225 extra soldiers have been deployed to the city to beef up security in the aftermath of the terror.
All public transport was temporarily shut down with Belgium hiking its terror threat to its highest level following the strikes.
Security at key locations and transport hubs has also been stepped up across the UK, Netherlands, France and Germany.
Acting Taoiseach Enda Kenny informed the House here that there are no indications of Irish injuries in the Brussels attacks.
The Department of Foreign Affairs has upgraded its threat level for Irish people in Belgium, advising extreme caution.
Aer Lingus and Ryanair are facilitating passengers who have been affected by events in Brussels.