Hany Saqr, the center's leader, has disputed Stemberger's charges, and there are no known law enforcement investigations of the center.
FBI officials told ABC News that none of the Noor Center's leaders have been charged with crimes related to terrorism.
The accusations add another layer to the complex custody issues surrounding where Bary should live. The case has drawn law enforcement, family services and politicians from Ohio and Florida into a debate over religion and family.
Florida's Republican Gov. Charlie Crist said in a statement he was grateful the teen has been allowed to stay in Florida, and his administration "will continue to fight to protect Rifqa's safety and well-being as we move forward."
Advocacy groups from across the nation have written letters to Judge Daniel Dawson regarding the custody decision, and the Florida Department of Law Enforcement has conducted an investigation into whether Bary would be in danger if she returns to her family in Ohio.
They will present their findings to Dawson, who will decide where the religious convert will live.
Bary, who was born in Sri Lanka and came to the United States in 2000, secretly converted to Christianity at a Columbus, Ohio, church in 2005 and prayed in secret, she said, hiding her religion for fear of her parents' retribution, and connected online with other Christians.
In an affidavit submitted before the custody hearing scheduled for today, Bary said her father confronted her in June after word of her religious conversion began to spread. Bary wrote that in July, her father said, "If you have this Jesus in your heart, you are dead to me! You are no longer my daughter."
Bary said she feared her parents would be forced to kill her for leaving Islam, and that is why she ran away, taking a bus to Orlando, where she lived with the husband and wife pastors Blake and Beverly Lorenz, who she met through a Facebook prayer group for the couple's non-denominational Global Revolution Church.
"It's an honor [killing]. If they love God more than me, they have to do this. And I'm fighting for my life," Bary WFTV.
In an earlier interview on "Good Morning America," McCarthy disputed that, saying, "Neither Mr. or Mrs. Bary have ever threatened the life of their daughter, and patiently await their daughter's safe return."
But Bary's lawyer told ABCNews.com that the girl is in danger.
"There is a clear and present threat to Rifqa Bary's life if she is returned to Ohio," he said.
In a statement released last month, her parents blamed their daughter's claims on the influence of the pastors who took her in.
"To anyone's knowledge, Rifqa never told anyone that she was frightened while living with her parents in Ohio. Those words only came out of her mouth after being missing for two-and-a-half weeks and surfacing in the tight embrace of Mr. Lorenz, who had not promptly reported that the runaway had been in his home," the parents' statement read.
The girl stayed with the pastors in their Orlando home for two weeks before authorities were notified of her whereabouts.
Columbus police have questioned the validity of Bary's "honor killing" claims.
Mohamed Bary "comes across to me as a loving, caring, worried father about the whereabouts and the health of his daughter," Sgt. Jerry Cupp, chief of the Columbus police missing persons bureau. told The Associated Press.
Bary's mother and father, who traveled to Florida last month to fight for their daughter's return, are expected to ask Dawson to send their daughter to Ohio.