The rampage by a knifeman in the heart of Britain's seat of power began on Wednesday, when he mowed down pedestrians on Westminster Bridge before stabbing to death a policeman inside the gates of Parliament before being shot dead by other officers.
US president Donald Trump was quick to offer his support, tweeting: "Spoke to UK Prime Minister Theresa May today to offer condolences on the terrorist attack in London. She is strong and doing very well."
White House spokesman Sean Spicer said London and the British government had the "full support" of the US.
In France the Eiffel Tower went dark in mourning and solidarity with Britain.
Paris mayor Anne Hidalgo, whose city has suffered deadly extremist attacks in recent years, announced that the tower was turning off its twinkling lights at midnight.
Three French teenagers on a school trip were among those injured in Wednesday's attack.
French president Francois Hollande offered condolences to Mrs May for those who died in the attacks and expressed his country's solidarity with Britain "in this tragic ordeal".
"The British and French services are in close contact to conduct the investigation," he added.
"We are all concerned with terrorism. France, which has been struck so hard lately, knows what the British people are suffering today."
Mr Hollande added that countries "must bring all the conditions to answer these attacks" and that "it is clear that it is at the European level, and even beyond that, that we must organise ourselves."
German chancellor Angela Merkel said she learned "with sorrow" of Wednesday's incident and her thoughts were "with our British friends and all of the people of London", in particular those who were injured.
"I want to say for Germany and its citizens: we stand firmly and resolutely by Great Britain's side in the fight against all forms of terrorism," she said.
New Zealand's prime minister Bill English said he had written to British counterpart Theresa May to express support for her government and to offer his country's condolences to the victims' families.
Australian prime minister Malcolm Turnbull said the police presence at the Australian Parliament House had been increased in response to the London attacks.
"Australia's heartfelt sympathy and resolute solidarity is with the people of the United Kingdom with whom we stand today as we always have in freedom's cause," he said. "Staunch allies in the war against terrorism.
"The attack on the British Parliament is an attack on parliaments, freedom and democracy everywhere."
Spanish prime minister Mariano Rajoy sent a telegram to Mrs May, saying: "An execrable terrorist act like the one that took place today is a reminder that we face complex challenges for the security of our societies.
"We must remain united against these type of threats that affect all of us equally and that know no barriers."
Israel, which that has faced a wave of Palestinian attacks since 2015, also expressed solidarity with the victims of the London attack.
Deputy foreign minister Tzipi Hotovely said: "Israel expresses its deep shock at the terror attack in London and its solidarity with the victims and with the people and government of Great Britain.
"Terror is terror wherever it occurs and we will fight it relentlessly."
The Italian interior ministry said the nation's security and intelligence chiefs would be meeting in Rome on Thursday for "an evaluation of the terrorist threat".
The department said interior minister Marco Minniti convened the Committee of Strategic Anti-terrorism Analyses following "the tragic facts in London".
Italian security was already on high alert for a European Union summit bringing bloc leaders to Rome on Friday for a meeting with Pope Francis at the Vatican, and a ceremony in the Italian capital on Saturday.
Authorities are bracing for possible violence during several marches on Saturday, drawing thousands of both pro-and anti-EU participants.
Russian Foreign Ministry spokeswoman Maria Zakharova underlined the need for global co-operation in the fight against terrorism.
"We don't split terrorism into categories; we consider it as absolute evil," she said.
"At this moment, as always, our hearts are together with the British people, we feel their pain and speak again about the need to confront that evil."
Five South Koreans in their 50s and 60s were among the 40 injured when they were caught up in a stampede of people trying to escape the attack, the country's Foreign Ministry said.
Four of them suffered broken bones and other injuries and a woman in her late 60s needed an operation for a head injury.
Romania said two of its citizens were wounded in the attack.
Chinese premier Li Keqiang said the attack was the first subject of discussion when he met Mr Turnbull in Canberra.
Mr Li said "together, we send our condolences to the prime minister of the UK and together we condemn terrorism and we stand against all forms of terrorism".
He said "there cannot be continued instability in the world", adding: "We must cherish peace and stability."
China said one of its citizens was among the injured and urged Chinese nationals in the UK to avoid crowded areas or travelling alone at night.
The Chinese embassy in London said it was in touch with the family of the injured person.