Police say a lone male attacker carrying an improvised explosive device was responsible for a bombing at Manchester Arena.
The explosion at the end of a sold-out Ariana Grande concert has killed 22 people and injured 59 others.
Prime Minister Theresa May says many of those are being treated for life-threatening conditions.
Children are among those who died, Greater Manchester Police chief constable Ian Hopkins has confirmed.
Investigators are trying to establish whether the attacker, who also died at the scene, was part of a wider network.
In a statement from Downing Street after an hour-long emergency COBRA meeting, Mrs May said the police and security services believe they know the identity of the attacker – but they are not releasing his name at this stage.
The Prime Minister added: “It is now beyond doubt that the people of Manchester and of this country have fallen victim to a callous terrorist attack – an attack that targeted some of the youngest people in our society with cold calculation.”
She said the bomber “deliberately chose the time and place to cause maximum carnage” – adding that the attack stood out for its “appalling, sickening cowardice”.
A detailed forensic search is under way at the arena, and nearby Manchester Victoria train station will remain closed “until at least the end of today”.
Several young people have been reported missing following the explosion, with worried friends and relatives appealing for information on social media.
Footage from inside the venue showed fans running and screaming after the explosion, which happened at about 10.35pm on Monday.
A hotline has been set up for those with concerns over loved ones who remain unaccounted for. Those worried about their friends or family should call 0161 856 9400 or 0161 856 9900.
Ariana Grande, who was not harmed in the attack, tweeted: “broken. from the bottom of my heart, i am so so sorry. i don’t have words.”
Her manager, Scooter Braun, said they mourned “the lives of children and loved ones taken by this cowardly act”.
Concertgoers affected by the terror attack were offered shelter by residents, taxi drivers gave free rides and a hotel near the venue took in dozens of children.
Ch Const Ian Hopkins confirms children among the dead at arena blast
‘I can confirm that there are children among the deceased’
Andy Burnham, the mayor of Greater Manchester, said: “It is hard to believe what has happened here in the last few hours and to put into words the shock, anger and hurt that we feel today.
“These were children, young people and their families that those responsible chose to terrorise and kill. This was an evil act. We are grieving today, but we are strong.”
Home Secretary Amber Rudd also condemned the “barbaric attack, deliberately targeting some of the most vulnerable in our society”.
Burnham: ‘This was an evil act’
Major political parties have suspended General Election campaigning until further notice, and flags in Downing Street have been lowered to half-mast in honour of those killed and injured.
Labour leader Jeremy Corbyn said: “I am horrified by the horrendous events in Manchester last night.
“My thoughts are with families and friends of those who have died and been injured. Today the whole country will grieve for the people who have lost their lives.”
White House Press Secretary Sean Spicer says President Trump has spoken with the Prime Minister to offer “condolences and support on behalf of the US”.
In the capital, the Metropolitan Police has urged people to stay “vigilant” and added: “You’ll see more police in London today.”
This is the worst terror attack in the UK since 56 people were killed in the 7/7 London bombings in 2005.