They claimed that devotees climbing chariots and touching deities during rath jatra had been a long-standing practice in Puri temple.
The Daitapatis have also threatened not to cooperate with the SJTA in performing rituals.
SJTA chief administrator Aravind Padhee said: “We will hold discussion with the daitapatis.”
SJTA had before this year's rath jatra, decided not to allow devotees to climb chariots.
But, it had to change the decision in the face of the stiff opposition from Daitapatis.
The Sankaracharya Matha's functionaries, however, said that the seer's recommendation was based on religious scriptures.