Prime Minister Theresa May confirmed that the "terrible incident in London" was being treated as "a potential act of terrorism".
London Mayor Sadiq Khan said the attack was "a deliberate and cowardly attack on innocent Londoners and visitors to our city enjoying their Saturday night," adding: "There is no justification whatsoever for such barbaric acts".
Prime Minister Theresa May confirmed that the "terrible incident in London" was being treated as "a potential act of terrorism" and said she would hold emergency ministerial talks later in the day.
Andy Burnham, newly elected mayor of Manchester -- where a suicide bomber killed 22 people on May 22 at a concert by US singer Ariana Grande -- said: "Terrorism will not break us."
Opposition Labour Party leader Jeremy Corbyn: "Brutal and shocking incidents reported in London. My thoughts are with the victims and their families. Thank you to the emergency services."
Scottish Nationalist Party leader Nicola Sturgeon: "Dreadful news from London. My thoughts are with all those affected."
Chancellor Angela Merkel: "Today we are united across borders in horror and mourning, but also in determination," she said in a statement. "For Germany, I reiterate that in the fight against all forms of terrorism, we are resolutely at Britain's side".
President Donald Trump: "Whatever the United States can do to help out in London and the UK, we will be there - WE ARE WITH YOU. GOD BLESS!"
State department called the assaults "cowardly attacks targeting innocent civilians" and added: "The United States stands ready to provide any assistance authorities in the United Kingdom may request."
Ariana Grande, who was to be joined by stars including Justin Bieber and Katy Perry at a benefit show in Manchester Sunday night less than 24 hours after the London attack, tweeted simply: "Praying for London."
President Vladimir Putin "expresses his profound condolences for the British people and condemns the terrorist attack carried out hours ago in London," Kremlin spokesman Dmitry Peskov told Russian news agencies.
Turkish Prime Minister Binali Yildirim : "This treacherous attack once again highlighted that cooperation in the fight against all types of terror must be carried out decisively." Foreign Minister Mevlut Cavusoglu said: "Baghdad, Kabul and now London. We condemn terror wherever it happens. We shall defeat terror by a joint fight."
European Commission chief Jean-Claude Juncker, in letter to British Prime Minister Theresa May: "I know that the people of London will carry on defiantly, just like the people of Manchester showed us such a short time ago. The European Union, its Member States and its allies around the world will stand with them in solidarity."
President Emmanuel Macron: "In the face of this new tragedy, France is more than ever at Britain's side. My thoughts go out to the victims and their loved ones."
Prime Minister Justin Trudeau, during a reception with parliamentary press, said: "Canadians stand united in sending our love and support to our friends in London."
Arab League chief Ahmed Aboul Gheit called for "immediate and strong action from the international community" in order "to break the forces of terrorism and extremism" which "represent one of the biggest challenges the contemporary world faces".
Prime Minister Mark Rutte: "London is in mourning, once again, after a cowardly attack. And we are in mourning with her. Our thoughts and our heart are with the victims and their families".
Pope Francis: "May the Holy Spirit bring peace to the whole world, cure it of the plagues of war and terrorism, which even last night in London has struck innocent civilians.
"Let us pray for the victims and those close to them."
Prime Minister Paolo Gentiloni: "In memory of the victims and the injured, we stand together in a shared commitment to combatting terrorism.
"You are not alone," Foreign Minister Angelino Alfano said.
Prime Minister Malcolm Turnbull: "Prayers and resolute solidarity are today as always with the people of Britain in the face of the shocking terrorist attacks in London."
Prime Minister Bill English: "New Zealand's thoughts are with the victims of today's attack, along with their families and friends. Our hearts go out to you. Too many lives are being taken by terrorists set on inflicting pain and suffering on innocent people."