Burkhard said the victim, Alex Madrid of Albuquerque, and the suspect, Brandon Villalobos of Meadow Lake, had been in the Meadow Lake area near Los Lunas on and off since Monday, and Villalobos led law enforcement officials to Madrid's body Tuesday, the Albuquerque Journal reported Thursday.
No motive was given for the slaying, but officials said Madrid died violently.
Burkhard said Madrid's mother, Roxanne Madrid, reported her son missing Tuesday afternoon after discovering he was missing when she went to pick him up at Villalobos' home.
Deputies questioned Villalobos, who "was telling some pretty wild tales," the sheriff said. Although Villalobos did not confess to anything, he led deputies to a field near his home, where they found Madrid's body.
Villalobos also was charged with tampering with evidence.
Burkhard said Madrid died from "severe trauma." He declined to say what may have caused that trauma, but did say it was "a violent death."
Madrid was visiting with family in the Meadow Lake area.
Roxanne Madrid said the teens had an on-again-off-again friendship, saying Villalobos typically caused the rifts.
"Alex just wanted to be his friend," Roxanne Madrid told the Journal Wednesday in a phone interview. "Why? Why would Brandon do that to my son?"
KRQE-TV, Albuquerque, reported that court documents indicated Villalobos admitted to getting into a fight with Madrid, saying he hit Madrid once after Madrid attacked him with a screwdriver.
Albuquerque television station KOAT reported that Villalobos' father said the teenager suffers several mental health conditions.