The suspect in the armed attack on the Wal-Mart store in El Paso, Texas, on Saturday, is a 21-year-old white man from Allen, Texas, a suburb of Dallas, 1046 km east of El Paso, On the Rio Grande on the opposite side of the city of Ciudad Juárez across the US border with Mexico.
Several media reports quoted law enforcement officials as saying the suspect was Patrick Crosias.
Elgin police chief Greg Allen said the authorities were examining a statement from the suspect that "there is a possible link to a hate crime." Officials declined to give details and said the investigation was continuing.
But the four-page statement, posted on the often used 8-chan website, which is believed to have been prepared by the suspect, described Wal-Mart's attack as "a response to the Spanish invasion of Hispanics."
He also expressed support for the militant who killed 51 people in two mosques in Christchurch, New Zealand.
CNN said the FBI had launched an internal investigation into terrorism in connection with the incident.
It was the eighth-worst mass shooting incident in recent American history after the 1984 incident in San Isidro, in which 21 people were killed.
The state governor confirmed that the attack killed 20 people and said the authorities would deal with the incident as a murder and a hate crime.