His wife and two children had been missing since Monday, and the police had searched his home and scoured the surrounding area with K-9 units. Mr. Watts said in the seven-minute interview that he and Ms. Watts had had an “emotional” discussion before her disappearance, but he declined to go into detail.

Ms. Watts’s body was found on the property of Anadarko Petroleum Corporation, an oil company where Mr. Watts had worked, the authorities said at a news conference on Thursday. Bodies believed to be those of the two children were later found nearby, the police said that night.

Anadarko said Thursday that Mr. Watts was fired on Wednesday, the same day he was arrested. “We are heartbroken by this, and our thoughts and prayers are with the loved ones and friends of the Watts family,” a spokeswoman said.

A news report from Denver7, the ABC affiliate that interviewed Mr. Watts at his home, said that Mr. Watts had confessed to the crimes Wednesday night. The police would not confirm on Thursday that he had confessed.