The confessed shooter in the mass killing in the Texas border city, 21-year-old Patrick Crusius, 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 be exemplary.... It should serve as an example that human beings must end such acts. These irrational acts of extreme hate are not good for the United States or any country."
Crusius published an online manifesto before the August 3 shooting in which he vowed to fight a "Hispanic invasion" of the US. When he later confessed to the killings, he 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 comments referring to Mexican immigrants as criminals and rapists.