Watts spoke to investigators for five hours inside of the Wisconsin prison where he is being held.
In an interview that aired this week, Steven Lambert, a lawyer for the firm, told Dr. Phil that he believed the latest account from Watts.
He ultimately pleaded guilty to all three deaths and now says it was investigators themselves that planted that initial fiction in his mind.
In the interview, Watts detailed moment-by-moment accounts of the murders of his wife and daughters.
DENVER-Lawyers for the parents of a Colorado woman killed by her husband say he did so after she threatened to keep him from seeing their children because he wanted a divorce. Watts is heard telling investigators in an audio recording of the interview.
He admitted to strangling his wife, Shanann, in their bed, before driving her body and Bella, 4, and three-year-old Celeste to a worksite where he smothered the girls using a blanket, according to documents released today. He said detectives were the first to mention that Shanann may have killed their children and he "just went with it".
He was sentenced to life in prison for murdering his wife Shanann and their daughters, 4 year-old Bella and 3 year-old Celeste.
Earlier, Bella had walked into the room just after Watts had strangled his wife, Shanann, and was wrapping her in a sheet to dispose of her body.
Authorities have speculated that Watts wanted a chance to start over with the woman.
The interview also reveals that Watts loaded Shanann's body in the backseat of his truck with their two daughters. Irate, Watts jumped on top of her on their bed and straddled her.
Eerily and inexplicably, Watts said he mourns his dead wife and daughters daily.
Shanann Watts and her two daughters in an undated file
Watts says that triggered him into a rage. When he went inside, Celeste also was awake.
Watts denied the relationship but said he felt "more guilty than ever before" and told Shanann he didn't think the marriage was going to work. "What are you doing with Mommy?"
Then he smothered the girls one by one and dumped them in an oil tank - with little Celeste as his first victim, according to the report.
He also told police that his four-year-old daughter Bella walked into his bedroom holding her blanket, asking what was wrong with her mum; he told her that Shannan wasn't well.
He woke up a few hours later, he said, and made a decision to confront her about their relationship issues while she lay in bed.
Watts insisted that he did not plan to kill his wife or children.
"With Shan'ann I never felt like I could be myself", he said.
"Watts told agents he still looks at photos of his family in prison and still deosn't understand how it happened".
Lawyers from the Colorado public defender's office, which represented Watts, did not respond to requests for comment about the prison interview, including questions about whether Watts' account was accurate and why he chose to share the information now. Colorado prison officials moved him out of the state but have refused to confirm his location.
The alleged details surfaced when investigators met with convicted killer Chris Watts on February 18 at the Dodge Correctional Institution in Waupun, Wisconsin.
"I trusted you to take care of them, not kill them", Shanann Watts' father, Frank Rzucek, read in a statement at Chris Watts' sentencing hearing in November. He keeps photos of his wife and daughters in his cell and talks to them "every morning and every night".
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