An Irish citizen was among those hurt in the terror attack
The Islamic State has claimed responsibility for the Westminster attack, the Amaq news agency - which is linked to the group - has announced.
The attacker was described as a "soldier of the Islamic State".
In a tweet, the agency said: "A soldier for the Islamic State carried out the operation in answer to calls to target the people of coalition states."
The phrasing suggests the attacker was inspired by Islamic State, and had not been directly trained by it.
It has been confirmed that an Irish citizen was among those injured in the attack in London on Wednesday.
Foreign Affiars Minister Charlie Flanagan says his department has, through the Irish embassy in London, offered and stands ready to provide consular assistance.
Four were known to have died, after the death toll was revised from five by London's Metropolitan Police based on the latest information.
They include two members of the public - a woman in her mid-40s and a man in his mid-50s - a police officer and the attacker himself.
Scores of others were hurt, with 29 people still hospitalised - seven in critical condition.
The woman has been named as mother-of-two Aysha Frade (43) who was on her way to pick up her children from school when she was killed on Westminster Bridge.
Mrs Frade was born in Britain, but her mother was born in Betanzos, near the Galician city of La Coruna in north Spain, and her father was of Cypriot origin.
Her two sisters run a large language academy in Bentanzos.
Mrs Frade taught Spanish at DLD College London, based close to the scene of the attack, where she was described by the principle as "a highly regarded and loved" member of staff.
Her family in Spain are making their way to London and are expected to arrive later today.
American visitor Kurt Cochran has also been named as a victim.
Mr Cochran was visiting London from his native Utah as part of his wedding anniversary celebrations with his wife of 25 years Melissa.
The couple were due to return to the United States on Thursday.
Melissa is said to be in hospital with a broken leg, rib and a cut on her head.
The British Prime Minister Theresa May has made a speech in the House of Commons about the attack.
"Yesterday an act of terrorism tried to silence our democracy - but today we meet as normal.
"As generations have done before us and as future generations will continue to do, to deliver a simple message: we are not afraid. And our resolve will never waiver in the face of terrorism.
"We know that democracy and the values it entails will always prevail", she said.
"Those values free speech, liberty, human rights and the rule of law are embodied here in this place, but they are shared by free people around the world.
"A terrorist came to the place where people of all nationalities and cultures gather to celebrate what it means to be free. And he took out his rage indiscriminately against innocent men, women and children.
"Mr Speaker, this was an attack on free people everywhere and on behalf of the British people, I would like to thank our friends and allies around the world who have made it clear that they stand with us at this time.
"What happened on the streets of Westminster yesterday afternoon sickened us all."
Mrs May also confirmed the attacker was a British-born man who was known to police and MI5 intelligence services.
He was once investigated by MI5 in relation to concerns about violent extremism - with Mrs May calling him "a peripheral figure".
The attack began Wednesday as a man in a car drove into a number of pedestrians on Westminster Bridge, before crashing into railings and then running through the Houses of Parliament gates and stabbing a police officer.
The attacker, who was armed with two large knives, was killed after being shot by police. The officer - named as PC Keith Palmer - also died of his wounds.
Mark Rowley is the acting deputy commissioner at the Metropolitan Police.
He said: "Greater clarity is now developing regarding the casualty figures as we have now collated information from the public and five hospitals - the latest figures I have are that there are currently four dead and 29 people were treated in hospital.
"We are still collating numbers of walking wounded and of those in hospital sadly seven of them are in a critical condition.
“It is still our belief - which continues to be born out by our investigation - that this attacker acted alone yesterday and was inspired by international terrorism."
He also says raids have been conducted overnight at six addresses, and police made seven arrests.
The Westminster Parliament and Scotland Yard both held a minute silence before commencing business Thursday in memory of the victims.
Speaking on Wednesday night, Mrs May condemned the "sick and depraved" attack.
She praised the "exceptional bravery" of police and security services during the attack, and also paid tribute to the emergency services as a whole.
She insisted any attempt to defeat the values parliament stands for was "doomed to failure".
Mrs May ordered flags to be lowered to half mast over Downing Street as a mark of respect to the innocent victims of the attack.
A British government minister gave first aid to Keith Palmer, the unarmed police man who was stabbed to death outside Westminster Parliament.
Tobias Ellwood, whose brief includes anti-terrorism, performed mouth-to-mouth resuscitation on the officer.
The Tory MP and former army officer also tried to stem the flow of blood from the injured police officer, working with emergency services to try to save the officer's life.
He was photographed with a bloodied face after he was among those who tried to save the officer, who later died.
The politician, whose brother was killed in the 2002 Bali bomb attacks, told The Sun: "I tried to stem the flow of blood and give mouth to mouth while waiting for the medics to arrive but I think he had lost too much blood.
"He had multiple wounds, under the arm and in the back."
The officer had been stabbed by a suspected terrorist, who moments earlier had driven a car into a number of pedestrians on Westminster Bridge.
Eyewitness Hugh Dickinson, a 21-year-old student from High Wycombe, posted a picture of the minister on Twitter, showing him with a bloodied face but saying "he looked to be fine".
Mr Dickinson said: "He had blood on his forehead as you can see but he wasn't bleeding profusely."
One woman who was at the scene of the attacks Wednesday, Susan, said: "I think we all expected it to happen or something like it to happen. He's just a madman.
"It really shows how well our gun laws work here. I know it's bad but all he had was knife.
"Imagine he had one of those big rifles like you see in America? That'll probably happen eventually though."