The teen also sent a picture of his dead mother to his girlfriend, and met her and her grandmother at the church where his father used to work, according to charging documents.
It wasn't immediately clear if that contact avoided further bloodshed. But a statement of probable cause says Griego spent time at the church, first talking to his girlfriend and her grandmother and then meeting with the church pastor and a security guard.
Church officials called authorities, and Griego initially told arriving officers he had come home Saturday morning after spending time at a friend's house to discover his family dead.
The teen later confessed to shooting his mother because he "had anger issues" and was annoyed with her, the charging document said. He said he killed his siblings after they woke up and became upset, then grabbed his parents' assault rifle and waited in the downstairs bathroom to ambush his father.
After killing his father, Griego said he reloaded the guns so "he could drive to a populated area to murder more people," according to the statement.
His plan, the statement said, was to "shoot people at random and eventually be killed while exchanging gunfire with law enforcement."
Bernallillo County sheriff's officials planned a midmorning news conference Tuesday to release more details in the case.
Griego, meanwhile, remained in custody on charges of murder and child abuse resulting in death. He was arrested Saturday at his family's home in a rural area southwest of Albuquerque.
Detectives spent two days collecting evidence and trying to piece together what led to the attacks.
"There's no other way to say it, except that we have a horrific crime scene down there that we are working on," Bernalillo County Sheriff Dan Houston said Sunday.
The detectives had finished their work at the home by Monday afternoon. The metal gate at the home's entrance was shut, a small bouquet of purple flowers was on the top of the gate, and at each side there were religious signs, including one that read "Jesus is the reason for the season."
The sheriff's office identified the victims as Greg Griego, 51, his wife, Sarah Griego, 40, and three of their children: a 9-year-old boy, Zephania Griego, and daughters Jael Griego, 5, and Angelina Griego, 2. All appeared to have gunshot wounds to the head.
A sheriff's detective questioned the teen Saturday night, and the details of their conversation were spelled out in the statement.
The teen allegedly told the detective that he took a .22-caliber rifle from his parents' closet around midnight Saturday and shot his mother in the head while his younger brother slept next to her.
Griego told the detective that his brother woke up but did not believe him that their mother was dead, so he showed his mother's bloody face to his brother and then shot him, according to the statement.
The teen is accused of then shooting his two young sisters after they began crying in their room, and retrieving a military-style semi-automatic rifle from his parents' closet and waiting in a downstairs bathroom for his father to come home. The statement said he shot his father multiple times after he passed the bathroom doorway.
Greg Griego was a pastor who had once served at Calvary, one of Albuquerque's largest Christian churches. He also was well-known throughout the law enforcement community for his work as a voluntary chaplain.
Neighbor Terry Wootan described Greg Griego as a man with a big heart. The two sometimes chatted at the mailbox and would wave to each other when passing by. Wootan said Griego told him about his time in California when he was involved in gangs and how he turned his life around and found God.
"What he wanted to do was help people, and he would never quit," Wootan said.
The pastor's death has shocked the community, including the Albuquerque Fire Department and the Metropolitan Detention Center, where he volunteered his spiritual guidance.
A records check by the Children, Youth and Families Department indicated no problems with the Griego family and that Nehemiah Griego had never been in trouble with the law.
Sheriff's Deputy Aaron Williamson confirmed there was no history of any emergency calls to the home in the recent past.
According to the probable cause statement, Nehemiah Griego first told a staff member at Calvary that his family was dead and that he placed the two rifles in the family van as protection before driving to the church. He later changed his story, according to the detective's statement.
Asked if he had told anyone else about killing his family, Griego allegedly told the detective that he had taken a picture of his dead mother and sent it to his girlfriend.
The teen could make his first court appearance in the next day or two.