Police swooped down on the residences of Karni Sena Chittorgarh unit President, Govind Singh Khangarot, and Vice President Kamlendu Singh Solanki at 11 p.m. on Tuesday and arrested them.
Police also arrested Devendra Singh, one of the main members of the organisation.
"Police are trying their best to curb our protest," said Rajpratap Singh, state media in charge Karni Sena, speaking to IANS.
"We are not being allowed to take out a rally or stage protest. There is 'nakabandi' all around and strict police arrangements have been made in this town," he said.
"We have called a meeting and will unveil our next phase of action by evening after a call taken by our Chief Lokendra Singh Kalvi," he added.
"If we want, we can choose violent ways and disturb people and tourists. However, on the contrary, our women have decided to opt for jauhar (mass immolation) without disturbing anyone," he said.
He claimed that "wood has been collected at the jauhar location and 1,908 women have registered for jauhar. If the administration allows us to climb on top of the fort, we will do so."
The film releases on Thursday. The Karni Sena and other fringe groups claim Bhansali's period drama distorts history.