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 in Bethlehem.
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.
The French Prime Minister, Edouard Philippe, called on French citizens 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 Prime Minister Theresa May.
Mayor of Nice Christian Estrosi, said on 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, 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.
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, 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 and my best wishes to injured for a quick recovery".
- 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".