The group issued a generically-worded statement on its official propaganda channels on Monday morning saying the stabbing was carried out by an Isis “soldier”.
It said he was responding to calls for attacks on citizens of countries bombing Isis territories, which have since been lost in Syria and Iraq.
Isis’s statement contained no new details of the attack or the perpetrator, meaning it may have been based on media reports rather than direct communication with Sudesh Amman.
The terrorist organisation has claimed numerous attacks without proof, including the Fishmongers’ Hall stabbing in November.
Amman had been jailed for collecting and distributing terrorist material, and his trial heard that he had declared a pledge of allegiance to Isis.
Prosecutors said he had a “fascination with dying in the name of terrorism”, discussed carrying a knife attack and listed becoming a martyr as his top life goal.
He posted a photo of a knife and two guns on top of a black Islamist flag, with the caption “armed and ready 3 April” before his arrest, but was not charged with preparing an act of terrorism.
Amman was handed a three year and four month sentence in December 2018 for disseminating terrorist material and collecting information useful for terror attacks.
He was released last week after serving half of his jail sentence, after a total of 20 months in custody since his original arrest.
Amman's, mother Haleema Faraz Khan, told Sky News that he was a “nice, polite boy” who had seemed “normal” when she visited him at his probation hostel on Thursday.
She said he had become more religious since being in prison, and that she believed he had been radicalised while in HMP Belmarsh.
“He became more religious inside prison, that's where I think he became radicalised,” she added.
“He was watching and listening to things online which brainwashed him.”
Concerns have frequently been raised about terrorist networking inside the prison.
Ms Khan also said that Amman, the eldest of her five sons, had also developed extreme views after looking at Islamist material online.
His 2018 trial heard that he had started collecting terrorist material online at the age of 17 and was active on Telegram - then Isis's main platform.
The Metropolitan Police said he was being followed by undercover officers as part of a “proactive operation” when he launched his knife attack in a busy shopping street on Sunday afternoon.
He stabbed two people, who survived, before being shot dead by police.
Like other recent Isis-inspired attackers, Amman was wearing a fake suicide vest that ensured police would shoot to kill.
The former head of counterterror police warned that “more dangerous people” are now being released from British prisons than returning from Syria.
There are currently more than 200 people jailed for terror offences in the UK, but up to 800 flagged as potential extremists and prison officers fear the real number is far higher.
Recent cases have shown that terrorists are able to network and radicalise others inside prisons, and may be faking apparent compliance with deradicalisation schemes.
The government recently announced a package of new terror measures including lie detector tests for released terrorists and changes to make them serve longer in jail.
Further proposals were to be announced on Monday but there are mounting concerns that imprisoning extremists could actually be increasing the risk they pose because of a lack of control and effective deradicalisation work.
British security services have foiled 24 attack plots – 16 Islamist and eight far-right – since March 2017.
But the head of counterterror police has admitted that softer targets and more simple plots have become harder to stop.
In 2014 a speech by Isis's spokesperson called for indiscriminate attacks on all non-Muslims, particularly in countries including Britain in the US-led coalition bombing its territories.
Isis propaganda called for supporters to attack soft targets, such as shopping districts, with low security. Such attacks have been difficult for security services to intercept, because of the speed of planning and use of everyday items like kitchen knives.