A series of terrorist attacks in the Belgian capital left at least 30 people dead and 230 injured on Tuesday, with the Islamic State extremist group claiming responsibility for the explosions at a subway station and Brussels' international airport.

The Sunni jihadist organization, which controls swathes of territory in Iraq and Syria, said a group of its "soldiers" had attacked "carefully selected targets" in "crusader Belgium, which has not stopped attacking Islam and its people."

Belgium is part of the US-led coalition that has carried out airstrikes against Islamic State.

The group threatened further attacks on members of the coalition in a statement posted on social media by supporters and described by the US-based monitoring group SITE Intel as a "formal communique." It said that "what is coming will be harsher and bitterer."

But top Belgian officials appeared unfazed.

"I want to tell ... those who have chosen to be barbaric enemies of liberties, of democracy, of fundamental values that we will stay united, that we will be fully mobilized ... with a full determination to act to protect our liberties, our ways of living," Prime Minister Charles Michel told journalists in Brussels.

"We will continue to respond together with firmness, with calm and dignity," King Philippe added in a televised address to the nation.

Belgian prosecutors said they think two men managed to carry out a suicide bombing, while a third suspect caught on video surveillance is being sought with the public's help.

The first attack, in which two consecutive explosions occurred in the airport's departure hall around 8 am (0700 GMT), left at least 10 people dead and some 100 people injured, according to an initial estimate by Belgium's crisis centre.

The second explosion at the Maelbeek metro station, which went off at around 9:15 am in a subway train stopped in the station, left at least 20 people dead and some 130 injured, the crisis centre said.

The US State Department said it cannot confirm Islamic State's claim of responsibility but noted that the group is "capable of this sort of depravity." US President Barack Obama has offered Belgium support in its investigation.

People had already started laying flowers in the centre of the Belgian capital on Tuesday as the northern European country began three days of national mourning.

In the hunt for the perpetrators, police found an explosive device containing nails, chemical substances and an Islamic State flag during a raid in the Brussels neighbourhood of Schaerbeek, federal prosecutors said Tuesday evening, without providing further details.

Police spent much of the day searching for weapons and suspects in the sprawling airport building, located about 15 kilometres from the Brussels centre.

There were a total of three bombs used during the airport attack, but one did not explode, the governor of the Flemish Brabant province, Lodewijk De Witte, was quoted by the Belga news agency as saying. The bombs contained nails, an official from a hospital treating some of the victims told Belga.

Around 1,000 people were present in the airport hall during the attack, the news agency reported. Six police officers were among those injured.

Access to the airport was blocked after the attack, but 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 crisis centre said there would be no incoming or outgoing flights until at least noon on Wednesday, while the chief executive of the airport said it would remain closed until Thursday.

The public transport network in Brussels was also shut down for most of Tuesday, although it was coming back online by the evening. Train traffic to and from the Belgian capital was resuming too. Schools were expected to be open on Wednesday.

Military reinforcements have been deployed and controls are being carried out at Belgium's borders, Michel said.

The country raised its threat alert level to 4, indicating a "serious and imminent" threat. The EU institutions and the NATO military alliance, which are both headquartered in Brussels, also increased their threat levels.

Belgium had already been on high alert since the arrest in Brussels last week of Salah Abdeslam, a key suspect in the Paris terrorist attacks. Federal prosecutor Frederic Van Leeuw said it was too early to establish a link between the attacks in Brussels and Paris.

French Prime Minister Manuel Valls is expected in Brussels on Wednesday for a long-planned visit to the European Commission.

The president of the EU's executive, Jean-Claude Juncker, said that the attacks "touch us but do not scare us." The commission's main building is less than 500 metres from the Maelbeek station.

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