Finn is the highest-ranking U.S. Catholic cleric to be found guilty in the church's long-running child sex abuse scandal, The Kansas City (Mo.) Star reported.
The bishop was convicted this month on one count of failing to report child abuse suspicions regarding the Rev. Shawn Ratigan, who pleaded guilty in August to five federal counts of producing or attempting to produce child pornography.
The National Survivor Advocates Coalition, a national Catholic organization with headquarters in Dayton, Ohio, on Sunday demanded the bishop step down from his post.
"A criminally convicted bishop cannot lead. Bishop Finn must resign or be removed by Pope Benedict," chairwoman Kristine Ward said. "Every hour he remains bishop re-victimizes survivors and their families."
Jack Smith, a spokesman for the diocese, declined to comment on the call for Finn's resignation.
"The bishop continues to be focused on his work," he said.