John Stemberger, attorney, conservative Christian activist and leader of the Florida Policy Council, said the mosque, Noor Islamic Cultural Center, has ties to terrorists.
That "matter" was Rifqa's conversion to Christianity.
She ran away July 19, saying her father, Mohamed Bary, 47, had threatened to kill her.
The Barys do pray at Noor, the girl's father said, but it's not clear that Noor is a threat to Rifqa.
It is one of the most liberal mosques in the city, according to Columbus-area Muslims. It sponsors blood drives, a food pantry and next month, a health clinic.
Earlier this month, it hosted a day-long interfaith session on homeland security that was sponsored by the Ohio Department of Public Safety.
A hearing is scheduled Thursday in Orlando about what to do with the girl. Stemberger said he wants her to stay with a Christian foster family here until next August, when she turns 18.
When asked Monday to name people at Noor who want Rifqa dead, Stemberger did not, saying "the totality of circumstances present a danger to her."
There were radical Muslims in Columbus, including three who are now serving federal prison terms for conspiring with suspected terrorists to blow up the Brooklyn Bridge, a Columbus-area shopping mall and unspecified targets in the U.S. and Europe.
Those men -- Iyman Faris, Nuradin Abdi and Christopher Paul -- worshipped at another Columbus mosque near the Ohio State University campus, according to Fred Alverson, spokesman for the U.S. attorney's office in Columbus.
Neither he nor FBI Special Agent Harry Trombitas would say whether Noor, its members or leaders are under investigation for terrorist-related activities.
In a sworn affidavit, Rifqa alleges her father demanded to know what her religious beliefs were in an angry confrontation.
"If you have this Jesus in your heart, you are dead to me! You are no longer my daughter. . . . I will kill you! Tell me the truth!" the affidavit reads.
Bary says he did not threaten his daughter. He says he loves her, wants her to return and will allow her to practice whatever religion she likes.
Police and child welfare workers in Columbus who have talked to the girl's family say they seem to be reasonable people whose chief concern is the safety of a runaway child.
Hany Saqr, a physician and chairman of Noor, said last week did not know the Bary family, that when he searched mosque records, he found that Rifqa had attended classes there two years ago for about three weeks. What has happened to the family, he said "is really very sad."
Stemberger, in a 35-page pleading he said he filed Monday, alleged that Saqr was listed in the 1992 phone directory that ties him to the Muslim Brotherhood, a group Stemberger described as "responsible for birthing virtually every terrorist organization in the world, including al-Qaida."