Vettel stopped Clark, and told him that, to accept the plea, he must hear an admission of guilt.
"On May 7, I purposely killed my wife," Clark replied, with no evidence of emotion.
"Was it planned?" Vettel asked.
"Yes. I planned to do it that night."
Vettel then noted the facts of the case, as he knew them from a previous suppression hearing in which four separate confessions made by Clark to police were ruled admissible.
Vettel said he understood Clark was afraid his estranged wife was going to take the youngest of their 13 children out of state. So he borrowed a brother's truck and another brother's .22 -caliber rifle and went to her home with the express purpose of killing her, and then himself.
The gun did not fire, and he then used it to hit her repeatedly. It was destroyed in the attack, and he could not use it to kill himself, Vettel said.
"Yes, that's right," Clark said.
Sentencing is set for 10 a.m. Wednesday, the day his jury trial was scheduled to begin.
Police said Clark, 44, on May 7 beat his estranged wife, 43-year-old Carolyn Clark, in the head with the stock of a rifle in front of the youngest five of their 13 children.
Clark earlier had pleaded innocent by reason of insanity, meaning he did not know right from wrong at the time of the killing because of mental illness. The trial was scheduled to start next week.
Vettel ruled in October that Clark was mentally competent to assist his defense and on Dec. 22 denied a motion by Clark's court-appointed attorney, Hobart Shiflet, to suppress a recording of a confession Clark made to police after his arrest.
Mrs. Clark had won custody of the children days before her death. Eight are now in county custody. Legal papers she filed in the custody dispute accused leaders of the couple's church of sexual and physical abuse against members, including children.
Clark said she was trying to get her young children away from the church, which she accused of brainwashing her husband and older children. The older children have often attended court hearings to support their father.
Prosecutors looked into the church and its bishop, Charles Keyes, but found nothing, Sartini said.
"We heard all kinds of rumors, but we found no evidence the church was complicit in her death," Sartini said.
Social service officials are looking into the abuse allegations against the Apostolic Church Body of Jesus Christ of the Newborn Assembly, which has denied wrongdoing.