Mrs May said: "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".
Speaking outside Downing Street after chairing a meeting of the government's Cobra emergency committee, May condemned the "cowardice" of the attacker and hailed those who rushed to help, who had shown "the spirit of Britain.a spirit that through years of conflict and terrorism has never been broken and will never be broken".
Liberal Democrats leader Tim Farron, who has cancelled a planned visit to Gibraltar, said: "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".
"We struggle to comprehend the warped and twisted mind that sees a room packed with young children not as a scene to cherish but as an opportunity for carnage".
"It is the worst attack the city has experienced and the worst ever to hit the north of England".
At least 22 people, including children, were killed and dozens more were hurt in the attack, which left concertgoers screaming and prompted a massive police response.
In what appeared to be an unrelated incident Tuesday, police evacuated a large shopping center in Manchester that was rebuilt after an IRA bombing in 1996.
Jeremy Corbyn has said this was "the most awful and traumatic time" as "there can be nothing worse than losing a child in a situation like this".More news: Gael Clichy set to leave Manchester City this summer
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Greater Manchester Police said they arrested a 23-year-old man suspected of links to the attack, while a second man was detained at the city's Arndale shopping centre but was "not now believed to be connected to last night's attacks".
May will be travelling to Manchester today to be briefed by the city's mayor, Andy Burnham, and security services in the city.
It is believed the attack was carried out by a lone male suicide bomber who was carrying an improvised explosive device.
White House press secretary Sean Spicer said President Donald Trump, who is now on a visit to Israel, is being updated on the situation.
Grande, who was unharmed and safe following the attack, expressed her sadness over the attack. From the bottom of my heart, I am so so sorry.
Australian Prime Minister Malcolm Turnbull also remarked how young numerous victims could be. She also said 400 police officers have been working all night to calm the chaos.