Theresa May has said the “callous terrorist attack” in Manchester, which left 22 dead, was one of the worst ever experienced in British history.
The prime minister said the bombing was an act of “sickening cowardice” with young people having been deliberately and indiscriminately targeted.
Labour leader Jeremy Corbyn said the country should “not allow this violence to divide us”.
General election campaigning has been suspended until further notice.
Saying her thoughts and prayers were with the families of those killed and the injured, the PM said there would be difficult days ahead but Britain’s “spirit will never be broken… terrorists will never win and our way of life will always prevail”.
Speaking in Downing Street, she said it was “beyond doubt” that the attack at the Ariana Grande concert, in which children were among the dead and more than 50 people were injured, was “among the worst terrorist incidents we have ever experienced in the UK”.
“All acts of terrorism are cowardly attacks against innocent people but this attack stands out for its appalling, sickening cowardice, deliberately targeting innocent and defenceless young people,” she said.
Mrs May said the police were working to establish the full facts and although they believed they knew the attacker’s identity, this would not be confirmed while they investigated whether he acted alone or had been helped by others.
After her Downing Street address, the prime minister travelled to Manchester. Speaking after meeting Greater Manchester Police Chief Constable Ian Hopkins, she praised the “great spirit of Manchester” and said the police and security services had the resources to investigate the attack.
She is expected to lead another emergency response meeting of ministers, police officers and security officials – known as a Cobra meeting named after Cabinet Office room in which they meet – later on Tuesday.
Mr Corbyn, who spoke to Mrs May overnight, said he “totally and unreservedly condemned this appalling act of violence”.
Praising the emergency services who were helping people during this “terrible and traumatic time”, he said the country must come together and “not allow this violence to divide us or prevent us from leading a decent and normal life”.
SNP leader Nicola Sturgeon said the news was “heartbreaking” and her thoughts were with the victims of the “barbaric” attack.
Announcing it would not be going ahead with its manifesto launch as planned, the party tweeted: “Our thoughts are with Manchester.”
The Lib Dems, UKIP, Green Party and Plaid Cymru have also announced that they will be ceasing campaigning until further notice.
Lib Dem leader Tim Farron, who cancelled a planned visit to Gibraltar, praised the “great bravery and heroism” of the emergency services
“This is an attack on innocent people and the nation is united both in its grief and its determination to stand up to this deplorable attack,” he said.
UKIP leader Paul Nuttall said his thoughts and prayers were with those affected while Green Party co-leader Jonathan Bartley said “for young people to be targeted in this way is utterly atrocious”.
Tuesday’s Cobra meeting was attended by senior ministers, including Foreign Secretary Boris Johnson, police officers and intelligence officials.
Speaking before the meeting, Home Secretary Amber Rudd said the attack had “deliberately targeted some of the most vulnerable in our country”. She praised the emergency services for their response to the incident.
Union flags are flying at half mast in Downing Street as a mark of respect while the BBC announced that a series of Andrew Neil TV interviews with party leaders would be halted while campaigning was suspended.
Foreign leaders have also expressed their condolences and solidarity with the UK in the face of the global terror threat.
US President Donald Trump, who is on a trip to the Middle East, said the “slaughter of innocent people, mostly innocent children” was wicked and the work of an “evil loser”.
He called on all “civilised nations to join together to protect human life” and rid violent extremism and terrorism “from our society for ever”.
French President Emmanuel Macron said: “After last night’s attack in Manchester, it is clearly all of Europe – all of free Europe – that has been attacked. It is European and British youth which has been attacked in its heart.”
Jean-Claude Juncker, the president of the European Commission, said those wanting to “instil fear and sow division” would not prevail.
“Today we mourn with you,” he said. “Tomorrow we will work side by side with you to fight back against those who seek to destroy our way of life. They underestimate our and your resilience.”
Australian Prime Minister Malcolm Turnbull said his country stood with the UK “as we always have and always will, steadfast allies in freedom’s cause”.