The three were placed under an order preventing them from meeting a lawyer, and will be brought for a remand extension at the Magistrate's Court in Nazareth on Sunday.
They are represented by Honenu attorneys Adi Kedar and Aharon Roza, who appealed against the order to the Magistrate's and District courts in Jerusalem.
"This unusual order is reserved for serious security offenses only, and not for property offenses like the one in this case," Honenu said in a statement.
The Shin Bet said Sunday that a covert investigation led them to the three suspects.
The church, which Christians believe is where Jesus performed the Miracle of the Multiplication of the Loaves and the Fishes, lies on the shores of the Sea of Galilee and is a traditional site of pilgrimage in the Holy Land.
A spokesman for the fire brigade said a preliminary investigation showed the blaze broke out in several places inside the church, evidence that it was started deliberately.
Police initially arrested 16 youths, all yeshiva students from West Bank settlements, but released them shortly after.