US President Donald Trump has called those behind the Manchester suicide bombing and other similar attacks "evil losers in life".
"I won't call them monsters because they would like that term. I will call them losers," he said in a speech during a visit to the Middle East.
World leaders have been sending messages of grief and solidarity to the UK city after the explosion at an Ariana Grande concert on Monday night.
Twenty-two people have been killed.
One of the most poignant reactions came from Polish President Andrzej Duda, who laid flowers at the British embassy in Warsaw as it emerged that a Polish couple were missing.
Angelika and Marcin Klis had gone to the Manchester Arena to pick up their daughter Alex and have not been seen since. She has appealed for help in finding them.
French Prime Minister Edouard Philippe called on people to be vigilant.
"The most cowardly form of terrorism has struck once again, targeting - as in Paris more than a year ago - a concert venue," he said in a statement, referring to the attack at the Bataclan music venue in Paris in November 2015.
French President Emmanuel Macron, who also expressed condolences, plans to speak with UK Prime Minister Theresa May.
Mayor of Nice Christian Estrosi, told French television that the attack had reopened wounds for victims of the 2016 truck attack in the southern French city, which was claimed by the so-called Islamic State group and killed more than 80 people.
He said the people of Nice relive the pain "every time some of our friends are hit".
In an interview with France Info, Mr Estrosi assumed an Islamist motive, saying: "We must wage war against the fifth column which crawls like an octopus through underground networks."
In his remarks in the West Bank town of Bethlehem, Mr Trump also spoke of an "evil ideology [which] must be completely obliterated".
"Our society can have no tolerance for this continuation of bloodshed," he said during his press conference with Palestinian leader Mahmoud Abbas.
Manchester Police have not yet released details about the attacker or his motive, but they say they are treating it as terrorism.
Meanwhile Viktor Ozerov, who heads the defence committee of Russia's upper house of parliament, called the bombing a "lesson" to British special forces for refusing to co-operate with their Russian counterparts.
He said: "We have said several times, although the UK was the first country that refused to co-operate with us at the level of intelligence services, that we are ready to share any information we have. And now, of course, this applies."
Other reactions from around the world:
China's President Xi Jinping has also telephoned Queen Elizabeth, offering condolences to those affected, saying: "At this time of great difficulty the UK and China stand together"
Australian Prime Minister Malcolm Turnbull has expressed "heartfelt sympathy and resolute solidarity with the people of the United Kingdom"
Germany's President, Frank-Walter Steinmeier spoke of a "special bond with the British people at this tragic moment"
Donald Tusk, the European Council President, said late on Monday: "My heart is in Manchester this night. Our thoughts are with the victims."
Paolo Gentiloni, Italian PM: "Italy joins with the British people and Government. Our thoughts are with the victims of the #Manchester attack and their families"
Spain's PM Mariano Rajoy: "I condemn the attack. My condolences to the victims' families"
African Union Commission Chairman Moussa Faki Mahamat: "Africa stands with the people and government of the United Kingdom in reaffirming our solidarity with them during this difficult time"
A Vatican telegram read: "His Holiness Pope Francis was deeply saddened to learn of the injury and tragic loss of life caused by the barbaric attack in Manchester, and he expresses his heartfelt solidarity with all those affected by this senseless act of violence"