UK police have confirmed that 22 people have been killed - including children - and 59 injured after an explosion at Manchester Arena at the end of a concert by Ariana Grande.
Greater Manchester police said the perpetrator was a man acting alone, who died at the scene after detonating an improvised explosive device. Investigators are trying to establish whether the bomber was part of a wider network.
The blast took place outside the arena, in the public foyer, shortly after 10.30pm, minutes after the concert ended.
On Tuesday, the Commission lowered its flags at its Brussels HQ in tribute to the victims.
Commission President Jean-Claude Juncker issued a statement saying, "It was with great sadness and profound shock that I learnt of the brutal attack that struck Manchester.
"It breaks my heart to think that, once again, terrorism has sought to instil fear where there should be joy, to sow division where young people and families should be coming together in celebration.
"I would like to convey my deepest sympathies to Prime Minister May and to the British people.
"Today we mourn with you. Tomorrow we will work side by side with you to fight back against those who seek to destroy our way of life. They underestimate ours and your resilience - these cowardly attacks will only strengthen our commitment to work together to defeat the perpetrators of such vile acts."
UK Prime Minister Theresa May said, "We are working to establish the full details of what is being treated by the police as an appalling terrorist attack.
French President Emmanuel Macron has expressed his horror and distress at the attack. The Élysée Palace said Macron was planning to speak to Theresa May later on Tuesday.
In a statement, the recently elected French leader said he sent the British people France's "compassion and sorrow" and pledged to continue working with Britain to fight terrorism.
European Parliament President Antonio Tajani said he was "shocked by the deadly explosion in Manchester. Our thoughts and prayers are with the victims and families of those who have been injured."
This was echoed by EPP group leader Manfred Weber, who said he was "appalled by news of terrible Manchester attack. Our thoughts are with the innocent victims, their families and the UK people."
His Socialist counterpart, Gianni Pittella, said, "Our thoughts go out to all victims, their families and the British people."
ALDE group Chair Guy Verhofstadt said this was "a horrible and cowardly attack. Targeting our youth at a concert is a heinous crime but they will prove unity and hope always win."
Further comment came from GUE/NGL leader Gabi Zimmer who said, "We condemn in the strongest terms this attempt on the lives of innocent civilians attending a pop concert, a cowardly attack on people having an evening of music, joy and pleasure. We are horrified about reports of many adolescents and children being among the victims.
"We express our sincere condolences and support to the families of those affected and we stand in solidarity with our British friends and fellow citizens.
"The people of Manchester responded in the best possible way to the horrific attacks by coming together in solidarity, with heart-warming accounts of families opening their homes for the night and taxi drivers offering free rides to those stranded."