The statement posted online Sunday by the Amaq agency follows a pattern of Daesh-related media claiming responsibility for what appear to be the acts of individuals across Europe in the past few months.
CNN cannot independently confirm this latest claim.
"We still don't have anything substantive that would suggest anything more than what we know already, which is this was a lone attacker," St. Cloud Police Chief William Blair Anderson told CNN's Jake Tapper Sunday. "And right now, we're trying to get to the bottom of his motivations."
The FBI is calling the attack "a potential act of terrorism."
In response to local reports identifying the attacker as being of Somali descent, members of the Somali communities held a news conference Sunday expressing their grief for the victims and calling for unity.
Ahmed Said, executive director of the Somali American Relations Council, had previously disclosed that it was unclear if religion motivated the attack, "but we know he is Somali." Authorities have yet to confirm the attacker's ethnicity. CNN was also unable to confirm if he was Somali.
On Saturday, a Somali-American mother said she waited fearfully outside the mall Saturday, just like other citizens of the central Minnesota city, because her son was inside during the attack.
"This has been a dark day; it is a day we will never forget," said Lul Hersi. "Let us unite as one Minnesota... Please let's spread love instead of hate. Daesh does not represent us. It does not represent Islam, and it does not represent Somalis."
Police and witnesses said the man, wearing a private security company uniform, entered Crossroads Mall on Saturday night around 8 p.m. CT and attacked people.
St. Cloud Mayor Dave Kleis said three people remain hospitalized, including one person who is in a life-threatening condition.
Ashley Bayne, an employee of JCPenney at the mall, was visiting a coworker at the time of the incident.
"All of sudden chaos just broke out," she told CNN's Nick Valencia on Sunday. "There was a bunch of people running into the JCPenney mall entrance, and they were just screaming that someone was going around the mall stabbing people, and that there was blood everywhere. It was just honestly a really scary experience."
Bayne said she ran out to the parking lot and took off in her car.
The stabbings occurred in multiple locations inside the mall, including the common area and in several stores. The mall has security teams on site but they are not armed.
While the attacker was not identified, authorities said he'd had three previous encounters with police.