The young man killed by an off-duty police officer after he stabbed nine shoppers in a Minnesota mall in a suspected terror attack has reportedly been identified by his father as local community college student Dahir Adan.

Adan, 22, was born in Africa but has lived in the US for 15 years, his father, Ahmed Adan, told the Minneapolis Star Tribune. He said he had "no suspicion" of his son being involved in any terror activity.

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Adan said that police raided the family apartment in St Cloud, and seized photos and other materials, but noted that he didn't learn about his son's rampage in the nearby Crossroads Center mall until much later.

Isis has claimed the attack as its own, releasing an announcement on its newswire saying that the "executor of the stabbing attacks in Minnesota yesterday was a soldier of the Islamic State and carried out the operation in response to the citizens of countries belonging to the crusader coalition."

But it wasn't clear if Adan actually had any contact with anyone in Isis or if the organisation was simply claiming a "lone wolf" attack by a disturbed slasher.

Adan asked one victim if he was Muslim before attacking him, and was heard to invoke the name of Allah, said local police.

Law enforcement officials are currently treating the attack as suspected terrorism.

"We are currently investigating this as a potential act of terrorism," said the FBI's Richard Thornton, speaking at a news conference at the St Cloud Police Department headquarters. But Thornton did not link the attack to a specific terror group.

Police executed search warrants for two apartments, including the apartment where Adan lived with his father, officials said. Thornton said investigators are analysing the suspect's electronic records to determine a motive for the attack.

"We don't know if the suspect was in contact with or inspired by foreign terrorist organisations," he said.

The FBI's Joint Terrorism Task Force is working with police to analyse the suspect's social media and other contacts.

Police have yet to officially identify the mall attacker, but several Minnesota news outlets and Associated Press have named, and leaders of the Somali-American community in Minnesota have also confirmed his identity.

Community leader Abdul Kulane said as far as the family and community are aware, the suspect did not have any history of violence. He was known as a smart, accomplished student and was a junior at a local college, Kulane said. Adan was also working part-time as a private security officer, leaders said.

The suspect in the mall attack was wearing a security guard uniform.

He left the family home shortly before the attack and said he was going to the mall to buy an iPhone7, according to Kulane, the St Cloud Times reported.

Seven male and two female victims were stabbed, ranging in age from a 15-year-old girl to a 53-year-old man, said officials.

Three remained hospitalised as of early Sunday (18 September). None of the injuries was believed to be life-threatening.

The officer who fatally shot the suspect was identified as Jason Falconer, a local off-duty officer and former police chief in the nearby town of Albany.

"The officer's life was clearly in danger," said St. Cloud Mayor Dave Kleis. He pointed to a surveillance video that shows the officer shooting, and the suspect falling and getting back up three times, and at one point lunging toward Falconer.

Contacted by the Star Tribune, Falconer said: "I've been trying to stay away from it all, for the time being."

The attack was condemned by leaders of the Somali-American community, but they are also concerned about a backlash.

Jaylani Hussein, executive director in Minnesota of the Council on American-Islamic Relations, called the attack an "isolated incident."

Eleven Somali-Americans living in Minnesota have been charged since 2014 in an alleged plot to travel to Syria and join Isis.

Two were charged in absentia after they left the US, while six others pleaded guilty and three were convicted in May.