Nehemiah Griego, 15, was in the Bernalillo County Juvenile Detention Center, charged with two counts of murder and three counts of child abuse resulting in death.
The victims were identified as Greg Griego, 51, a former pastor at megachurch Calvary Chapel; his wife, Sarah Griego, 40; Zephania Griego, 9; Jael Griego, 5; and Angelina Griego, 2.
The Griegos had 10 children, but only the three youngest and Nehemiah were at home during the shootings early Saturday.
"I've never seen a scene quite like this," Bernalillo County Sheriff Dan Houston said during a news conference Sunday.
The Journal said sheriff's investigators found a number of weapons at the Griego home, including an AR-15 semiautomatic assault-style rifle and a .22 caliber pistol.
The Journal said it appeared Nehemiah had a minor argument with his mother Friday night, then waited for her to go to sleep. About 1 a.m. Saturday, he went into his mother's room and shot her multiple times, then shot his siblings multiple times, investigators said.
Police said they believe the teen waited until his father came home and then shot him muyltiple times.
After the killings, the youth put a loaded AR-15 rifle and a loaded shotgun into the family's van and drove off, planning to go to the nearest Walmart, where he would kill more people, police said.
He apparently planned to die in a gunfight with law enforcement officers but called a friend who convinced him to meet at Calvary Chapel, the Journal said.
Eventually, the teen told a church security guard someone killed his family at their home and the guard notified police, the report said.
Authorities said they believe Nehemiah's parents owned the guns, which were stored in a closet, not in a gun safe, the Journal said. They also said they thought the boy may have had violent fantasies for much of his life.
The location of the other children during the shootings was not reported.
"Our family is grieving this terrible tragedy," the family said in a statement. "We appreciate the prayers and support we have received and request that the media honor our family's privacy during this difficult time."