Mexico's Foreign Secretary, Marcelo Ebrard, has raised the possibility of seeking Crusius' extradition to face charges south of the border.
Crusius allegedly authored a racist manifesto and posted it online in the hours before the shooting.
Authorities said Crusius drove 11 hours from his hometown of Allen, Tex., near Dallas, to perpetrate a massacre in the predominantly Hispanic city of El Paso. (AP) Multiple people were killed and injured and at least one person was in custody after a shooting rampage at a shopping mall, police in the Texas border town of El Paso said.
In addition to the 22 people killed, more than 20 were wounded in the attack. Authorities say the mass shooting is being investigated as a hate crime and act of domestic terrorism.
Jessica Coca Garcia stands in front of her wheelchair addressing those gathered at the League of United Latin American Citizens' "March for a United America" Saturday, Aug. 10, 2019 in El Paso, Texas.
Crusius also waived his Miranda rights, including the right to remain silent, and is said to have spoken willingly with the police.
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The vehicle he emerged from on Saturday was about a half mile from the Walmart, stopped on a street that essentially divides shopping areas from residential areas.
On Friday, President Donald Trump, who travelled to El Paso earlier this week, pledged to take a "serious" look at passing new gun control measures to strengthen the background check system.
The alleged gunman was identified as Patrick Wood Crusius, 21. The officer also additionally inquired about the emotional state and intentions of the person who had ordered the weapon, police said. "He was raised in a family that taught love, kindness, respect, and tolerance - rejecting all forms of racism, prejudice, hatred, and violence".
He surrendered without incident, and has been speaking co-operatively with police since the attack, according to investigators in El Paso.
Mr O'Rourke said El Paso was "showing the world that hate has no home here".