The group is accusing America's largest Protestant denomination of also failing to root out molesters.
The Chicago-based Survivors Network of Those Abused by Priests — or SNAP — has started a campaign to call attention to alleged sex abuse committed by Southern Baptist ministers and concealed by churches.
The group presented a letter Monday to Southern Baptist Convention executive committee members in Nashville, Tenn., asking the group to adopt a zero-tolerance policy on sex abuse and to create an independent review board to investigate molestation reports.
Church leaders concede there have been some incidents of abuse in Southern Baptist congregations, but say their hands are tied when it comes to investigating complaints across the denomination.
One such incident occurred this week in Columbia, S.C., where police said a pastor sent pornographic messages and obscene pictures of himself over the Web to a police officer posing as a 14-year-old girl.
Kershaw County Sheriff Steve McCaskill says 42-year-old Kevin Ogle has agreed to go to Walton County, Georgia, to faces charges.
Authorities say Ogle chatted on the Internet for three months with the Georgia officer he thought was a 14-year-old girl, exchanging sexually explicit messages and sending pornographic pictures of himself.
He has been charged with 11 counts of sexual exploitation of children.
Ogle is the pastor of Northgate Colonial Baptist Church.
"It's a bombshell, but it's nothing we can't overcome with God's help," said Deacon Mike Clifton told CBS affiliate WLTX correspondent Will Frampton. "Satan has thrown a stone at us, and we're gonna throw it right back."
Clifton said there's no question the church's congregation will forgive its pastor.
"We can't expect God to forgive us when we ask him for forgiveness, and not forgive our pastor, or any fellow man, when they do wrong."