"The executor of the stabbing operation in the city of Paris is a soldier of the Islamic State and the operation was carried out in response to the calls to target the coalition states", the SITE Intel group reported the Amaq Agency, ISIS's media wing, as having said.
The suspect is a 20-year-old man who was born in 1997 in Chechnya, the Muslim-dominated Russian republic, reports France24 News, citing judicial sources. When police officers arrived minutes later, he threatened them and was shot dead, police union official Yvan Assioma said.
In the Paris apartment of the parents Asimov on Sunday at dawn, also were searched, according to AFP.
Now though, ISIS have released a propaganda video featuring the killer in which he recorded a last message confirming his affiliation with the terror cell.
It took place in the heart of the French capital in an district renowned for the Paris opera and many landmark retail stories.
Chechnya's president identified him on Sunday as Khamzat Azimov.
Here is a recap of jihadist attacks that have killed more than 245 people across France since the 2015 Charlie Hebdo shootings.
The Russian Embassy in France said it has requested more information on the attack suspect.
Beyond the police cordon, however, crowds still filled nearby cafes and the city's night life resumed its normal pace soon after the attack.
"What good does this S file do if we don't use it to get these ticking time bombs off French soil", far-right leader Marine Le Pen posted on Twitter.
The Paris prosecutor's office, which handles all terrorism cases, is taking over the investigation.
A 54-year-old woman was also seriously wounded and recovering in hospital, while a 26-year-old woman and a 31-year-old man had slight injuries.
Less than twenty-four hours after a knife attack in central Paris killed one individual and injured four others, Archbishop Michel Aupetit on Sunday evening asked for prayers for "victims of hate", and urged Mass-goers to seek the intercession of a "God of love".
Islamic State has claimed responsibility for the assault, but it remains unclear whether the assailant was inspired by the terror group or had actual operational links with IS. "I heard two, three shots and a policeman told me that the man had been overpowered", he told AFP news agency.
"The attacker came down this road here with his hands covered in blood, holding a knife up in the air", Oliver Woodhead, owner of L'Entente Restaurant, told the outlet RT.
Authorities said Azimov stabbed several people during the attack. "Then I went out to see what was going on, and then I saw a man on the ground", she added. The scene "was kind of a mess", she said.
However, one man who works in the neighbourhood where the rampage occurred saw a grim pattern.