Donald Trump has offered Theresa May the full cooperation and support of the United States after the Westminster attack, that killed five people and injured at least 40 people.
The US president, who vowed to keep America safe from terrorism as one of his core his election pledges, praised "the effective response of security forces and first responders".
"[Trump] pledged the full cooperation and support of the United States Government in responding to the attack and bringing those responsible to justice," the White House said.
Trump told reporters shortly after the attack: "I was just getting an update on London. Some big news having to do with London just happened."
Trump's spokesman, Sean Spicer, added that "the city of London and Her Majesty's Government have the full support of the US government".
The full White House statement:
"President Donald J. Trump spoke today with Prime Minister Theresa May of the United Kingdom to offer his condolences on today's terror attack in London and his praise for the effective response of security forces and first responders. He pledged the full cooperation and support of the United States Government in responding to the attack and bringing those responsible to justice."
US Secretary of State Rex Tillerson said: "On behalf of the United States, I send my condolences to the victims and their families.
"The American people send their thoughts and prayers to the people of the United Kingdom. We condemn these horrific acts of violence, and whether they were carried out by troubled individuals or by terrorists, the victims know no difference," he said.
France sends 'message of friendship' to UK
French President Francois Hollande also called May and "conveyed the solidarity of France in this tragic ordeal", the Elysee Palace said.
France has been struck by several acts of terrorism over the past two years, including in Nice last July when a gunman drove a heavy truck into a crowd celebrating Bastille Day, killing 86 people and injuring scores more in an attack claimed by Islamic State.
Three French schoolchildren were injured in yesterday's attack on London.
France's new interior minister sent a "message of friendship" and "full solidarity to the British" people after the London attack.
"A high place of democracy has come under attack," said Matthias Fekl. "We offer our wholehearted solidarity to Great Britain. France is naturally ready to offer any support if that is needed," he said.
Three pupils from the Saint-Joseph high school in Concarneau in Brittany were among the injured, a spokesman for the French foreign ministry confirmed.
French Prime Minister Bernard Cazeneuve confirmed on Twitter that pupils had been injured. "Solidarity with our British friends who have been terribly hit, full support to the injured French pupils, their families and their classmates," he wrote.
Angela Merkel expresses shock at London attack
German Chancellor Angela Merkel expressed her shock at the attack and said her thoughts were with the British people and everyone in the capital.
She stressed that Germany was on the same side as Britain in terms of fighting terrorism. In December, a failed Tunisian asylum seeker pledging allegiance to Islamic State killed 12 people in Berlin by driving a truck into a crowded festive market.
"Although the background to these incidents still needs to be exactly clarified, I confirm on behalf of Germany and its citizens that we stand firmly and resolutely by Britain's side when it comes to fighting any kind of terrorism," she said.
German security officials said they remained on high alert for a possible attack, but there had been no change in security procedures.
Interior Minister Thomas de Maiziere said that the London attack was likely terror-related.
"It has not yet been definitely established what the motive for the brutal incident was. There are many indications that there was a terrorist background," de Maiziere said.
He added that German security authorities were in close contact with their British counterparts.
Dutch send support, and Geert Wilders highlights attack
Dutch Prime Minister Mark Rutte, who is still acting head of government while a new coalition is formed after elections last week, said he was "shocked" by images of the attack.
"We still know very little, but it is certain that people have been injured. Perhaps, it is to be feared, worse. The British can count on our support. We are monitoring the situation closely and are in contact with the British authorities," he wrote on Facebook.
Far-right Dutch PVV politician Geert Wilders retweeted the story running on national broadcaster the NOS, without comment.
Italy highlights importance of intelligence cooperation
Italian MPs said the attack demonstrated that intelligence cooperation between the UK and the rest of Europe must continue, despite Brexit.
"The London terrorist attack shows that European intelligence must not lower its guard, and cooperation between our countries must be strengthened, with or without Brexit," said Mariastella Gelmini, a former government minister and a senior member of the centre-right Forza Italia party.
The Italian parliament tweeted its "solidarity" with London and the UK Parliament. "Our thoughts and solidarity go out to London and the UK Parliament," the tweet said.
The Russian foreign ministry expressed condolences to the British people and urged its citizens in London to be vigilant.
"Our hearts are with the British, we share their pain," Maria Zakharova, a Russian foreign ministry spokeswoman, said on Russian state TV.
"We are calling on Russian citizens who are in Britain and on the grounds of our embassy in London to show vigilance and follow the official reports that will be published," she said.
Israel's deputy foreign minister Tzipi Hotovely expressed "deep shock" and "solidarity with the British people". Hotovely added that she had spoken with the British ambassador to Israel about the attack.
Polish media reported that a meeting between the British Prime Minister and Jaroslaw Kaczynski, the leader of Poland's governing party, had been either delayed or cancelled because of the attack.
Kaczynski, who was in London to discuss Brexit and security issues with May, was described as "safe" by a party spokeswoman.
Polish foreign minister Radoslaw Sikorski was on Westminster Bridge at the time of the attack and tweeted a video of the aftermath.
"A car on Westminster Bridge has just mowed down at least 5 people," he wrote. "My prayers are with the victims."
Canadian Prime Minister Justin Trudeau said: "Our thoughts are with the victims of today's attack in London and their families.
"Canadians remain united with the people of the UK."
Spanish Prime Minister Mariano Rajoy condemned the deadly attack and offered condolences to the British people in a telegram sent to May.
"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," said Rajoy.
"We must remain united against these type of threats that affect all of us equally and that know no barriers."