The Shin Bet internal security agency said Jerusalem resident Yitzhak Gabai, 22, and brothers Nahman (18) and Shlomo (20) Twitto of the ultra-orthodox Beitar Illit settlement were members of Lehava, an extremist group which fights against intermarriage.
On Sunday, police announced the arrest of several suspects in the torching of a classroom at the Hand-in-Hand school, a rare symbol of coexistence, without providing further details.
The Shin Bet said on Thursday the three had confessed, saying they had done it to "raise the issue of objection to coexistence and intermarriage to the top of the public and media's agenda".
Police said Lehava activists were tied to a number of other violent incidents.
Lehava leader Bentzi Gopstein said his organisation does not act illegally, accusing the Shin Bet in a statement of trying to frame Lehava to thwart its "holy work of saving the daughters of Israel".
The November 29 attack sparked a wave of condemnation and took place amid months of rising tensions and unrest in Jerusalem.
Israeli Prime Minister Benjamin Netanyahu and other senior officials condemned the attack at the school, which is on the Green Line separating west Jerusalem from the annexed eastern sector and has 624 pupils.
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