On Twitter, US President Donald Trump branded the shooting "an act of cowardice," adding, "I know that I stand with everyone in this country to condemn today's hateful act. There are no reasons or excuses that will ever justify killing innocent people."
Police said the suspect Patrick Crusius, 21, of Allen, Texas opened fire with a rifle on shoppers, many of them bargain-hunting for back-to-school supplies, then surrendered to officers who confronted him outside the store.
El Paso Police Chief Greg Allen said the suspect was cooperating with investigators.
Watch: United States bloody history of mass shootings
"He basically didn't hold anything back," Allen said at Sunday's news conference but declined to elaborate.
Texas Governor Greg Abbott said Saturday's rampage appeared to be a hate crime, and police cited a manifesto they attributed to the suspect as evidence that the bloodshed was racially motivated.