"Multiple weapons were apparently used, including one assault rifle," Bernalillo County Sheriff Dan Houston told reporters in a televised news conference.
Deputies responded to the house on Saturday night. The victims -- which included two girls and a boy -- were each apparently shot multiple times.
In a statement late Sunday, the sheriff's office identified the victims as Greg Griego, his wife Sara, and the children: Zephania, 9; Jael, 5; and Angelina, 2, the Associated Press reported.
Sheriff's spokesman Aaron Williamson confirmed to the Los Angeles Times that the suspect is 15-year-old Nehemiah Griego, who has been arrested and charged with two counts of murder and three counts of child abuse resulting in death.
One of those killed was Greg Griego, who was identified as Nehemiah's father in a biography that has since been removed from the website of the Albuquerque Calvary Church. A church leader told KOB-TV that Griego, a pastor, had taken a leave of absence from the church last year.
According to the biography, Greg Griego and his wife had 10 children.
Neighbor Peter Gomez told the Albuquerque Journal he often saw the family on walks through the neighborhood, adding that Nehemiah Griego “wore nothing but camouflage stuff."
Steve Stucker, a weatherman with KOB-TV in Albuquerque, identified himself as a friend of Greg Griego's in Facebook posts on Sunday and wrote that Griego's wife and three of their children were also killed in the Saturday slayings.
"Greg was an ex con and former Gangbanger who Completely turned his life around through his Faith in Jesus," Stucker wrote. "Greg, with the full support & blessing of his wife and family, spent the rest of his life visiting Jails & Prisons, sharing his story and changing Lives through the Love of Christ."
According to Griego's online biography, he began his religious service at the Calvary Chapel Montebello in California. He volunteered as a jail chaplain for years and was a volunteer chaplain with the Albuquerque Fire Department, which mourned him Sunday.
Albuquerque Fire Chief James Breen said in a statement that Greg Griego had a gentle and calming manner.
KOB-TV said Greg Griego was the brother of former state Sen. Eric Griego, and said the family had released a short statement: "Our family is grieving this terrible tragedy. We appreciate the prayers and support we have received and request that the media honor our family's privacy during this difficult time."
Stucker, the weatherman, also wrote on Facebook, "I can't pretend to speak for him...but I KNOW he would have asked us to Forgive the one who did this awful thing, because he never thought it was too late to change a person's heart & mind."