Scott Peterson Talks to ABC News' Diane Sawyer

— Scott Peterson, the husband of the missing pregnant Modesto, Calif., woman, says he didn't murder his wife Laci, but admits she knew about his affair with another woman.

Peterson told ABCNEWS' Diane Sawyer that his wife accepted his affair with Amber Frey, a single mom from Fresno, when he told her back in early December.

He says he and his wife never even had a fight over his extramarital affair, adding that he never laid a hand on Laci and hopes to find her alive.

"I had absolutely nothing to do with her disappearance," Peterson said. "And you used the word murder," he told ABCNEWS' Diane Sawyer on Good Morning Ameirca. "Yeah, I mean, that is a possibility. It's not one we're ready to accept and it creeps into my mind late at night, and early in the morning," Peterson said.

Peterson said he decided to speak out after a month of silence because the suspicion about his involvement in Laci's disappearance had distracted the public from the search.

He denies that his revelation of his affair led to any kind of physical confrontation with his missing wife.

Wife Not ‘OK’ With the Cheating

"You know, I can't say that even, you know, she was OK with the idea, but it wasn't — it wasn't anything that would break us apart," Peterson said.

In the one-and-a-half-hour interview with ABCNEWS, Peterson was composed at moments, and soaked in tears at others.

"In the morning I've been taking the dog down to the park where she walked," Peterson said. "It was our time. It's a way to experience her now, for me. A lot of times I can't make it very far," he said, crying.

Laci Peterson's family supported Peterson when his pregnant wife went missing Christmas Eve, but news of an alleged lover has left the missing young woman's family angry and skeptical.

"There's other questions we have that if he wasn't truthful about that, it makes us wonder if he's been truthful about everything else," said Laci Peterson's mother, Sharon Rocha, on ABCNEWS' Good Morning America Monday.

Peterson, who has not spoken publicly about the case until now, has been under close scrutiny by Modesto Police since they found difficulty corroborating his alibi, and more recently when it was discovered that he had been having an affair in the months prior to her disappearance.

Laci Peterson disappeared on Christmas Eve. The 27-year-old is due to deliver a baby boy in two weeks. While Modesto authorities say they have no suspects in the case, Laci's husband has not been eliminated as a suspect yet.

Peterson said Laci told him she was taking the family dog, McKenzie, for a walk at a nearby park before she disappeared. McKenzie was later found in the backyard, trailing a muddy leash.

Peterson says he understands that police immediately looked at him went Laci went missing.

"It's turned me, one, because I'm her husband," Scott Peterson said. "And it turned to me because of the inappropriate romantic [relationship] … that I had with Amber Frey."

Scott Peterson says he never loved Frey and can't even explain why he pursued a relationship with her or why he continued it after telling his wife.

"That's a question you should have an answer to definitely, and I don't know," Peterson said.

Despite the couple's problems, Scott Peterson said there was no anger or cruelty expressed between him and Laci.

"Violence towards women is unapproachable," Scott Peterson said. "It is the most disgusting act, to me."

In a press conference Friday night, Frey admitted that she had a romantic relationship with Peterson. When she discovered he was involved in the Laci Peterson disappearance case, Frey said she immediately called the Modesto Police Department on Dec. 30.