The victim, Jules Woodson, claimed that Savage assaulted her 20 years ago, when she was only a 17-year-old student.
His request for forgiveness got a standing ovation from the congregation.
He said before she went public with her story, he thought the issue had been "dealt with in Texas".
"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".More news: Pakistani Journalist working for Indian channel escapes abduction bid in Islamabad
The girl, identified as Jules Woodson, who was reportedly assaulted by Savage, recounts that she was in his vehicle with him as he was supposedly giving her a ride home, but he instead drove the vehicle to a remote location where he sexually assaulted her.
Woodson told The Times she found the round of applause for Savage "disgusting" and added the incident had not been properly "dealt with" because it was never was reported to law enforcement.
"Until now, I did not know there was unfinished business with Jules", Mr Savage said, in remarks live streamed on the church's YouTube page.
Monday, Christina publisher Bethany House announced they canceled the publication of Savage's book, The Ridiculously Good Marriage. For any painful memories or fresh wounds this has created for anyone, I am sorry, and I humbly ask for your forgiveness.More news: Oil prices sit at three-year highs as march to $70 slows
"I remember him pleading, while he was on his knees with his hands up on his head, 'Oh my god, oh my god".
"On behalf of the elders, pastors, staff, and Trustees of Highpoint, I want to affirm that we are 100% committed to Andy [Savage] ... and his continued ministry at Highpoint Church", Conlee continued, according to The Huffington Post. Savage responded in his message that the "incident" took place "more than 20 years ago" - as if the fact that it happened long ago makes it less consequential. "You have to take this to the grave with you.' He said that several times". She says he asked her to unbutton her shirt and to perform oral sex on him.
"I just hope that by me coming forward that I would give courage to one other person", Woodson said. After a few minutes, Woodson says Savage said he was sorry and pleaded with her not to tell anyone.
Woodson also told the newspaper she spoke on Monday with a detective in Texas, though it's not clear whether a statute of limitations would apply.More news: 'Black Panther' breaks Marvel's pre-sale record on Fandango
A Christian publisher has canceled the publication of Andy Savage's marriage book after it was revealed that the pastor sexually assaulted a teenager. She told the incident to their associate pastor Larry Cotton who was completely unsupportive and unsympathetic to her plight. The pastor, she said, turned down a dark road, where he parked the truck and turned off the headlights.
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