Amid reports that a third bomber involved in the attacks on Brussels had been arrested by Belgian security forces, European Commission president Jean-Claude Juncker pledged that the EU would "stand united" in the face of terrorism.
The EU chief said, "These attacks have hit Brussels today, Paris yesterday – but it is Europe as a whole that has been targeted.
"These events have affected us, but they have not made us afraid. We will continue our work, to face the terrorist threat together, and to bring European solutions to questions that concern us all."
The former Luxembourg PM also praised the Belgian security forces, emergency services and others who had helped victims and reassured EU staff "that their security remains a priority for me and that all possible measures will be taken."
Three commission staff were hospitalised in the blast while an EU office block that was badly damaged in the explosion at Maelbeek metro may have to be demolished for fear of it being at risk of collapse.
Other EU leaders responded with the European Parliament's president Martin Schulz speaking of his "horror" at the "despicable and cowardly" attacks in Brussels.
The German Socialist MEP said the atrocity "angered and saddened" him and was "born from barbarism and hatred which do justice to nothing and no one."
Expressing "compassion and solidarity" with the Belgian people, Schulz pledged that "Brussels, like other cities hit by such terrorist attacks, will stand strong, and the European institutions will do likewise.
His comments were echoed by Dutch Prime Minister Mark Rutte whose country is the current holder of the EU Council presidency.
Expressing his "revulsion", he said Belgium had been hit by "cowardly, murderous attacks" adding, "While many things are still unclear, it's certain that special vigilance is needed now, not only in Belgium but also in our own country. We will take all necessary precautions."
Several MEPs were also quick to react with UK Liberal Democrat Catherine Bearder saying she was "shaken" by the "horrific and cowardly attacks."
Ashley Fox, leader of the UK Conservatives in the European Parliament, said the attacks were "terrible" but that people "must carry on with their daily lives and not let the terrorists win. If we change our routines, or if we surround the Parliament with a ring of steel, we play into the hands of the people who committed these atrocities."
European Conservatives and Reformists leader Syed Kamall, another British MEP, condemned the "wicked and indefensible acts", adding, "They targeted people in Brussels but it could just as well have been in any of our cities or towns. People of all faiths, races and views today stand united to state that these terrorists may attack us, but they will never defeat us and our freedom, our pluralism, or our way of life."
Italian deputy Gianni Pittella, leader of the S&D group agreed, saying that European society could not be "overcome by fear" so that it creates a "fortress leading to even more ghettoization and marginalization."
He went on, "We must work together to keep our society united around common values and principles, and we must fight to eradicate xenophobia and islamophobia. We should question ourselves in asking why young Europeans devote themselves to fundamentalism and terrorism. We definitely should improve our model of cultural integration."
Elsewhere, GUE/NGL leader Gabi Zimmer said, "This is a black day for all of us. More than ever we will stick to our values of solidarity, peace and freedom."
The EPP group, parliament's biggest political grouping, issued a statement saying, "Our message today is: we'll do everything to protect the core values of our society with all our means. Europe will stand united against terror."
Reaction from other EU bodies was swift, with the Europol police agency's director Rob Wainwright saying the attacks were a "further reminder of the volatile terrorist threat faced in Europe today."
He added, "Working with its security partners in the EU and beyond, Europol is determined to fight terrorism in all its aspects and all its manifestations. To that end, our action must continue to be part of a comprehensive approach based on the strengthening of resources to thwart the actions of terrorist networks, their financing and online reach."
Civil society also condemned the atrocity but added a note of caution with the US-based Human Rights Watch calling on the Belgian authorities to respond with a "strong commitment to the rule of law and human rights" in their efforts to prevent further attacks and "possible acts of retaliation against communities and individuals."
A statement said, "We need to protect the human rights principles that extremists are flouting. That is our common challenge."
A spokesman for Brussels-based Social Platform called for more to be done to tackle the "root causes" behind such tragedies and the "rising tide of inequality and alienation."
Michael O'Flaherty, director of the EU Agency for Fundamental Rights, argued, "This attack is an attack on all of us. Every human has the right to life, and this right has been trampled on in Belgium's capital.
"At the same time, our reaction must not be one of hatred and fear – this would just play into the hands of the perpetrators. Our answer in the EU must be to stand by our belief in human rights and their universality."
Amnesty International believes the attacks demonstrated "utter contempt for human life."
In a statement, Philippe Hensmans, managing director of Amnesty International Belgium-Francophone Section and Han Verleyen, acting director of Amnesty International Belgium-Flemish Section, said, "To deliberately target civilian lives is, and always will be, inexcusable. Those responsible for these attacks must be brought to justice."
The Strasbourg-based Council of Europe also reacted by declaring three days of official mourning.
Bulgarian foreign minister Daniel Mitov, who chairs the organisation's Committee of Ministers, said Tuesday's events a "further attack against our democracies" and called on the West to "resolutely continue to combat terrorism in full respect of the values and principles that unite our continent."
Council of Europe secretary general Thorbjørn Jagland asserted that the attacks had targeted European values and Europe "has to stand together in fighting terrorism on the basis of human rights and the rule of law."
He noted, "Preventing radicalisation should be a priority and embrace education and working for inclusive societies."