The affidavit said inmate Byron Scherf acknowledged the crime to detectives Wednesday in a videotaped interview.
The interview came after Scherf asked detectives for a chance to tell them what happened, the affidavit said. He acknowledged his right to remain silent, then confessed.
"I'll just get right to the point. I'm responsible for the death of the correctional officer at the Monroe, uh, correctional facility," he said, according to excerpts cited in the affidavit. "I strangled her to death on Jan. 29 at approximately 8:40 p.m. in the chapel."
Scherf, 52, reportedly told detectives he was angry at Biendl over how she had spoken with him sometime between 8:15 and 8:25 while he worked in the prison chapel that evening. The content of the remarks Scherf claimed she made was not detailed in the affidavit.
"I became very angry ... and the more that ran through my mind the madder I got," Scherf was quoted as saying. "I got to the point where I knew I was going to kill her."
Scherf's public defender did not immediately return a call or e-mail seeking comment Friday.
According to the affidavit, Biendl sent the inmates back to their cells at about 8:30 and began closing the chapel. Scherf said he decided to hang back and attacked Biendl from behind, it said. He said he fought with her for three or four minutes, with Biendl trying unsuccessfully to radio for help, according to the document.
Scherf said Biendl bit and scratched him and stomped on his foot trying to get free. They wound up on the ground and he used a cable from an amplifier to fatally choke her, he reportedly told detectives.
He was described as becoming emotional as he said, "I'm certainly sorry."
The affidavit was written in support of a search warrant to look for blood, skin, sweat or other trace evidence that could corroborate Scherf's account.
The warrant is one of several made public in the last few days. One released Thursday said Scherf had asked others who attended the chapel to pray for him two days before the killing because he was struggling with temptation.
Scherf is a three-strikes offender serving a life sentence for rape convictions. He volunteered at the chapel where he worked as a janitor and clerk. He's jailed in Everett for the homicide investigation.
The search warrants make clear that detectives are preparing for a possible death penalty case.
Scherf has been serving life in prison without possibility of release since 1997 after he was convicted of three attacks on women.
The search warrants show investigators have been spending considerable time with Scherf since the killing. For example, they obtained a judge's permission to carefully photograph Scherf's nude body under special lights that make it easier to spot injuries, including hidden bruises.