"As a college student on staff at a church in Texas more than 20 years ago, I regretfully had a sexual incident with a female high school senior in the church", Savage said in his statement to Highpoint Church.
Woodson says she complied, and went along again when he took off her bra and touched her, but said she "was scared and embarrassed".
Instead, she writes, he drove down a dead end road, turned off the vehicle's lights, pulled his penis out of his trousers and asked her to perform oral sex on him. She then told the head pastor, Steve Bradley, who eventually talked to her mother but twisted the story so that it only seemed like Savage and Woodson had shared an "innocent kiss".
"Until now, I did not know there was unfinished business with Jules", Mr Savage said in a live streamed service.
According to Woodson's account, in spring 1998 she was hanging out with a group of kids at their church, Woodlands Parkway Baptist Church.
"It's disgusting", she told the newspaper, and argued that the incident had not in fact been "dealt with" as Savage said, because law enforcement never became involved, even though Woodson claims she reported it to the local sheriff department.
Chris Conlee, Highpoint's lead pastor, told church members Sunday before Savage spoke about the situation that the church was "1,000 percent" supportive of Woodson's healing as well as Savage.
Pastor Andy Savage has attacked homosexuality and advocated for the use of "conversion" therapy to attempt to change the sexual orientation of minors. I remember feeling special and excited, as in my mind, he obviously wanted to spend more time with me before taking me home. In agreement with wise counsel, I took every step to respond in a biblical way, ' he said.
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A woman wrote, "I support the Savage family..."
Savage explained to his Memphis followers that he immediately resigned from his Texas post after the incident.
I want other victims of sexual abuse, especially within the church, to know that they're not alone and to know that they have a voice.
The day she heard about Lauer's firing, Woodson said she sent an email to Savage asking if he remembered that day he drove her home in 1998.
Woodson said she was inspired to come forward by the global #MeToo movement against sexual harassment. "I had just been manipulated and used - I swore to him I wouldn't tell anyone just to get him to stop". This is after Savage confessed to sexually harassing a 17-year-old girl some 20 years ago. "He then told me not mention anything that had happened to anyone else", she wrote.
The Christian publisher Bethany House told the New York Times it was canceling the upcoming publication of Savage's self-help book The Ridiculously Good Marriage, initially scheduled to publish in July.
On her blog, Woodson recounted the alleged assault and how it emotionally scarred her.
Woodson also said she made a decision to come forward with the story after she saw a USA TODAY story in December about Matt Lauer being fired by NBC because of sexual misconduct.