The confessed shooter in the mass killing in the Texas border city, 21-year-old Patrick Crusius, potentially faces the death penalty in the US.
Lopez Obrador, an anti-establishment leftist, said that while Mexico condemns Crusius's "reprehensible, abominable" crimes, it does not want to see him put to death.
"Our constitution does not allow the death penalty. We do not want the death penalty, as a matter of conviction. Life imprisonment does not exist (in Mexico), either," he told a press conference.
"I have given instructions to explore the possibility of requesting this person's extradition," he added.
"We do not want impunity. We want the punishment to serve as an example.... Given that this was a premeditated crime, and all the aggravating factors, he would face a long time in prison in Mexico... more than 50 years."
Gunman kills 20, wounds 26 at Walmart store in El Paso, Texas
Mexico has said it considers the August 3 shooting at a packed Walmart store a "terrorist attack."
Crusius published an online manifesto before the shooting in which he vowed to fight a "Hispanic invasion" of the US. He later told police he had been targeting "Mexicans."
The shooting came at a time of already strained ties between the United States and Mexico, a frequent target of President Donald Trump's attacks.
Trump critics accuse him of stoking white nationalist hatred in the US with anti-immigrant rhetoric, including comments referring to Mexican immigrants as criminals and rapists.
The Mexican foreign ministry convened a meeting of Latin American diplomats on Friday to seek a joint response to what it called the threat of "white supremacism" to Spanish speakers in the United States.
"What happened in El Paso represents an inflection point in protecting Hispanic communities in the United States, given that it was a domestic terror attack, sustained by xenophobic rhetoric," Mexican Foreign Minister Marcelo Ebrard told the meeting.
Mexico has called on the US to reject the "rhetoric of hate" in the wake of the shooting.
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