British Prime Minister Theresa May told the House of Commons that the London attacker was British-born and earlier investigated by MI5 for links to violent extremism.
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May says police believe the man acted alone and there is no reason to believe "imminent further attacks" are planned.
"What I can confirm is that the man was British-born and that some years ago he was once investigated by MI5 in relation to concerns about violent extremism," she told lawmakers.
"He was a peripheral figure," she added. "The case is historic, he was not part of the current intelligence picture."
She said there had been no prior intelligence of his intent nor of the plot.
"When operational considerations allow, he will be publicly identified," she added.
Police arrested seven people as part of an investigation into the lone-wolf attacker who killed three people and injured 40 before being shot dead by police near parliament in London, Britain's most senior counter-terrorism officer said on Thursday.
Mark Rowley said there were four dead including the attacker and that 29 people, seven of whom are in critical condition, are still being treated in hospitals.
Police had said on Wednesday that the death toll was five in the worst such attack in Britain since 2005.
The attacker sped across Westminster Bridge in a car, ploughing into pedestrians along the way, and then ran through the gates of the nearby British Parliament building and stabbed a policeman before being shot dead.
Authorities have said they are working on the assumption that the attack was Islamist-related.
Britons have been shocked by the fact that the attacker was able to cause such mayhem in the heart of the capital equipped with nothing more sophisticated than a rented car and a knife.
"The police and agencies that we rely on for our security have forestalled a large number of these attacks in recent years, over a dozen last year," said Defense Minister Michael Fallon.
"This kind of attack, this lone-wolf attack, using things from daily life, a vehicle, a knife, are much more difficult to forestall," he told the BBC.
A minute of silence was held in the Parliament and in front of police headquarters at New Scotland Yard at 9:33 A.M. local time in honor of the victims – 933 was the shoulder number on the uniform of Keith Palmer, the policeman who was stabbed to death.
"We're dealing with an enemy, a terrorist enemy, that is not making demands or taking people hostage, but simply wants to kill as many people as possible. This is a new element to international terrorism," Fallon said.
Rowley said police had searched six addresses in London, Birmingham and other parts of the country in their investigation.
"It is still our belief ... that this attacker acted alone and was inspired by international terrorism. At this stage we have no specific information about further threats to the public," Rowley said.
He said there was a mix of nationalities among the dead but gave no details. The victims were the policeman, Palmer, and two members of the public, a woman in her mid-40s and a man in his mid-50s. The fourth dead was the assailant.
Three French high school students aged 15 or 16, who were on a school trip to London with fellow students from Brittany, were among the injured.
French Foreign Minister Jean-Marc Ayrault was expected to arrive in London to visit them in the hospital, French media reported.
There were also five South Koreans among the injured, South Korea's foreign ministry said in Seoul.
Prime Minister Theresa May was due to make a statement to parliament on the attack at 10:30 A.M. local time.
A vigil was planned in London's Trafalgar Square for 6 P.M.
Fallon said security arrangements at the Parliament would be reviewed.
A meeting of COBR, the government's crisis response committee, was due to take place later on Thursday morning.
Westminster Bridge remained cordoned off with a strong police presence. The nearby Westminster underground rail station, normally a busy hub in the morning rush hour, was not accessible from the street as it was within the cordon.
May said on Wednesday the location of the attack was not an accident. She said any assault on British values of liberty, democracy and freedom of speech was doomed to failure and Britons would not be divided by such acts.
But anti-immigration groups were quick to make links between immigration and the attack.
Leave.EU, a group that has campaigned for immigration to be severely restrained as part of Britain's exit from the European Union, accused mainstream politicians of facilitating acts of terror by failing to secure borders.
"We are sick, tired but perhaps even more so we are angry that recent governments across Europe have enabled these attacks through grossly negligible policies that have left us vulnerable," the group said in a statement.
In France, far-right presidential candidate Marine Le Pen also drew a link, saying that events in London highlighted the importance of protecting national borders and stepping up security measures.
The Scottish Parliament, which suspended a planned debate and vote on independence on Wednesday because of events in London, was due to resume those proceedings on Tuesday, the BBC reported.