Abdulahi Hasan Sharif, 30, is accused of running down a police officer with his car and then stabbing him repeatedly on Saturday night in Edmonton, Alberta.
Canadian Prime Minister Justin Trudeau called it a “terrorist attack” and said he was both “deeply concerned and outraged” by “this senseless act of violence”.
Police said Sharif fled before driving a U-Haul truck into four pedestrians while trying to escape.
US Immigration and Customs Enforcement (ICE) spokeswoman Lauren Mack said in a statement that Sharif was in custody in the United States for about four months in 2011.
He was ordered to be deported to Somalia but was released on an “order of supervision” in November 2011.
The statement said that Sharif did not appear for a scheduled meeting in January 2012 and efforts to locate him “were unsuccessful”.
ICE statement added: “Sharif had no known criminal history at the time of his encounters with ICE.”
Canadian Public Safety Minister Ralph Goodale said Sharif made a refugee claim at a Canadian border crossing in 2012 and obtained refugee status later that year.
In 2015, a complaint led police to probe Sharif’s alleged extremist ideology, but officers found no grounds for criminal charges despite an “exhaustive investigation”.
Mr Goodale said on Monday it would be wrong to blame the attack on any shortcomings in Canada’s immigration and refugee vetting system.
Sharif faces 11 charges including five counts of attempted murder.
He appeared via video in an Edmonton court on Tuesday wearing an orange jail uniform and he had bruises on his face, which police say he sustained while fleeing.
He had a Somali interpreter, although he did not speak.
Community leader Mahamad Accord did not speak to Sharif but learned about him from the local Somali community.
He said Sharif was from a Somali ethnic minority and was little known in the community.
He added: “Everyone who knows Sharif said this is out of character.
“There is a mental health issue, we suspect.”
Edmonton police did not immediately comment.
Sharif’s lawyer Chady Moustarah said he had stepped in on short notice to help someone without representation but that the accused would have to find another lawyer going forward.
Sharif remains in custody until his next court appearance, scheduled for Nov 14.