UK authorities identify the attacker as 52-year-old Briton, Khalid Masood.
Daesh was responsible for an attack outside Britain's parliament which left four people dead, excluding the attacker, the group's Amaq news agency said on Thursday.
What role Daesh did or did not play in the attack is unclear, although the group has exhorted its members and sympathisers to carry out such attacks as it continues to lose territories it seized in Iraq and Syria to local forces, regional allies, and a US-led military coalition.
A statement from the group said the attacker had "carried out the operation in response to calls to target citizens of the coalition."
British Prime Minister Theresa May described the incident as an attack on free people everywhere, and said the country would not be cowed by terrorism.
TRT World correspondent Jon Brain reports.
British police meanwhile named attacker as 52-year-old Briton Khalid Masood. They said the man was known to police and has a range of previous convictions for assaults, including GBH (grievous bodily harm), possession of offensive weapons and public order offences.
Masood was born in Kent to the southeast of London. Most recently, he was living in central England, London police said. None of his past criminal convictions were related to terrorism offences.
"Masood was not the subject of any current investigations and there was no prior intelligence about his intent to mount a terrorist attack," they said in a statement.
Earlier, Prime Minister May said the attacker had been investigated in the past for extremism, but he hadn't been considered a threat.
TRT World's Simon McGregor-Wood is in London with more.