Former Ukip leader Nigel Farage blamed what he called a "direct attack on children" on Islamic terrorism. The singer who performed at the manchester Arena yesterday, Ariana Grande, has a strong following of young fans.
Labour leader Jeremy Corbyn said his thoughts were with all those affected by the "terrible incident".
Tim Farron, the Liberal Democrat leader, condemned the "shocking and horrific" attack targeting youngsters.
In a message on Twitter, Corbyn said: "Terrible incident in Manchester. My thoughts are with all those affected and our brilliant emergency services."
Farron said: 'This is a shocking and horrific attack targeting children and young people who were simply enjoying a concert.
"My deepest sympathies are with the victims, and with families who have lost loved ones, as well as those desperately waiting for news."
The SNP also suspended campaigning and delayed the planned launch of its electoral manifesto.
Liverpool's Metro Mayor Steve Rotheram, whose daughters were at the Manchester Arena concert, said: "Feel sick to think that people have lost their lives at a gig attended by so many young people.
"All my thoughts go out to those parents waiting to hear of the safety of their children. It's a parent's worst nightmare. So, so sad."
SNP leader Nicola Sturgeon said: "Heartbreaking news from Manchester. My thoughts are with all those who have lost loved ones or been injured in this barbaric attack." Irish ambassador Daniel Mulhall said: "Horrified by what's happened in Manchester.
"My thoughts & deepest sympathies are with all those affected by this terrible tragedy."
Manchester City Council leader Sir Richard Leese said: "This is an absolutely horrifying incident and our thoughts are with everyone affected, especially those who have lost loved ones or been injured and traumatised.
"If it is confirmed this was a terrorist attack,it is monstrous act but also a deeply futile one. Manchester is a proud, strong city and we will not allow terrorists who seek to sow fear and division to achieve their aims.
'We give heartfelt thanks to our emergency services for their response and council staff are doing all they can to support."
Mayor of Manchester Andy Burnham said: "My heart goes out to families who have lost loved ones, my admiration to our brave emergency services.
"A terrible night for our great city."