British Prime Minister Theresa May has described the Westminster attack as "sick and depraved", she was speaking after chairing a special meeting of the Cobra committee following the deadly attack in Westminster today.
Mrs May praised the "exceptional bravery" of police during the attack and said any attempt to defeat the values that Parliament stands for are "doomed to failure".
At least 40 people were injured in the incident.
Britain's top anti-terrorism officer, Metropolitan Police Assistant Commissioner Mark Rowley, said police believe there was only one attacker, who was killed after being fired at by police.
Mrs May has ordered flags to be lowered to half mast over Downing Street as a mark of respect to those who lost their lives.
The Cobra committee brought together government ministers with senior officials of the emergency services and security and intelligence agencies.
The committee co-ordinates the high-level response to serious incidents, and has previously gathered after terrorist atttacks, including the 7 July, 2007 attacks on the London transport network and the murder of soldier Lee Rigby.
Among ministers attending this evening's meeting were Defence Secretary Michael Fallon, Security Minister Ben Wallace, Transport Secretary Chris Grayling, Health Secretary Jeremy Hunt and Foreign Minister Sir Alan Duncan.
Absent were Home Secretary Amber Rudd, who was away on an official trip to Pakistan, and Foreign Secretary Boris Johnson, in the US for a summit of nations involved in the fight against the Islamic State terror group.
The meeting in Whitehall was addressed byAssistant Commissioner Rowley.
Taoiseach and President pass on condolences
Taoiseach Enda Kenny took to Twitter to express solidarity and condolences.
"On behalf of Government I send our support to PM May & British people. Condolences to the families of the victims and thoughts with the injured," he said.
President Michael D Higgins is to write to Queen Elizabeth II and London Mayor Sadiq Khan to express the sympathy "of the Irish people with the families of those who have lost their lives and to those who have been injured".
President Higgins said he wanted to express "the sympathy, condolences and solidarity of the Irish people with our neighbours at this difficult time".
On behalf of Govt. I send our support to PM May & British people. Condolences to the families of the victims and thoughts with the injured.
— Enda Kenny (@EndaKennyTD) March 22, 2017
Minister for Foreign Affairs Charlie Flanagan also extended sympathies.
"I wish to extend my condolences and on behalf of my Government, my support to the people of London and the UK. Terror and violence will never triumph over democracy," he said.
No Irish are believed to have been caught up in the attack.
Trump pledges full co-operation and support
Meanwhile, the White House said US President Donald Trump spoke to Mrs May 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 co-operation and support of the US 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 express 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."
Three French schoolchildren injured in attack
French Prime Minister Bernard Cazeneuve expressed his solidarity with "our British friends" in the wake of the attack.
Three French pupils on a school trip were among those hurt when a car mowed down pedestrians on Westminster Bridge.
Local officials in the western region of Brittany, where the French students are from, said two of them were in serious condition.
French President Francois Hollande also sent a message of "solidarity" and "support" for Britons and Prime Minister May.
"France, which has been hit so hard in recent times, knows what the British people are suffering today," Mr Hollande said in a statement before news of the French injured emerged.
Germany's Merkel expresses shock
Elsewhere, German Chancellor Angela Merkel expressed shock at the attack and she said her thoughts were with the British people and everyone in London.
Ms Merkel 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 so-called 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 in an emailed statement.
German security officials said they remained on high alertfor a possible attack, but there had been no change in security procedures.
Interior Minister Thomas de Maiziere said that the London attack was likely a terrorist incident.
"It has not yet been definitely established what the motivefor the brutal incident was. There are many indications thatthere was a terrorist background," Mr de Maiziere said in an emailed statement.
He added that German security authorities were in close contact with their British counterparts
