The Islamic State has claimed responsibility for the Streatham stabbing attack.
The group's Amaq news agency put its name to the attack on Monday, without giving evidence.
"The perpetrator of the attack in Streatham district in south London yesterday is a fighter of Islamic State, and carried out the attack in response to calls to attack the citizens of coalition countries," a statement carried by Amaq said.
Sudesh Amman, 20, the suspect behind Sunday's attack, had previously praised the Islamic State, shared an online al Qaeda magazine and encouraged his girlfriend to behead her parents.
Amman, who was jailed for possessing and distributing terrorist documents in December 2018, had recently been freed from prison, and had been staying at a bail hostel in nearby Leigham Court Road for the past two weeks.
The 20-year-old was under police surveillance as he launched his attack, and was found to be wearing a fake suicide vest after he was shot.
In November 2018, he pleaded guilty to six charges of possessing documents containing terrorist information and seven of disseminating terrorist publications, for which he was sentenced to three years and four months in prison.
It was revealed during his trial at the Old Bailey that he sent extremist content to his younger siblings via a family WhatsApp group, and wrote comments including: "The Islamic State is here to stay."
The messaging thread, titled La Familia, featured images of Amman's siblings adopting similar poses to those publicised by IS supporters such as one-finger salutes and wielding weaponry, the BBC reported.
He also sent beheadings videos to his girlfriend, who he instructed to kill her parents, telling her: "If you can't make a bomb because family, friends or spies are watching or suspecting you, take a knife, molotov, sound bombs or a car at night and attack the tourists (crusaders), police and soldiers of taghut, or Western embassies in every country you are in this planet."
In other messages with her, Amman pledged his allegiance to Islamic State, also known as ISIS, and said he wanted to carry out acid attacks.
Elsewhere, he asked if he could have a knife delivered to her address and told her he considered ISIS to be the best thing to happen to Islam.
He was automatically released from HMP Belmarsh at the end of January 2020 after serving half of his sentence in custody.
He was under a curfew and had to wear a GPS tag coupled with exclusion zones such as ports and airports.
He was also forced to surrender his passport and had limited access to eletronic devices and restrictions on his internet use.
Sunday's atrocity follows the attack at Fishmongers Hall in the City of London in November, for which ISIS also claimed responsibility.
The group said Usman Khan, who killed two people and injured more during his knife rampage, acted on their behalf.
Again, they relayed the information through the Amaq news agency and, again, they provided no evidence of their claims.
Their message claimed Khan was "responding to calls to target the nationals of Coalition countries".
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