The sexual assault and murder of an 11-year-old girl near Shiprock, New Mexico, has reignited the debate.
Ashlynne Mike's mother is urging the Navajo Nation to opt in to the death penalty, particularly for crimes that involve children.
Southwestern tribe has long objected to putting people to death. The culture teaches that all life is precious.
Legal experts say the decision goes back to culture and tradition, past treatment of American Indians and fairness in the justice system.
Tribes have been able to opt into the death penalty for certain federal crimes on tribal land for decades, but nearly all reject it.
One federally recognized tribe, the Sac and Fox Nation of Oklahoma, has opted in.