The government of Madhya Pradesh, another state ruled by the BJP, is expected to follow suit, say top sources in the party's state unit.
Assembly elections are due in Rajasthan, Chhattisgarh and Madhya Pradesh later this year and the BJP is wary of a political backlash, given the recent protests by Dalit groups across the country against what they call a dilution of the law.
Both Rajasthan and Madhya Pradesh have also decided to file petitions seeking a review of last month's Supreme Court verdict that said government servants should not be arrested under the SC/ST (Prevention of Atrocities) Act without prior sanction and private citizens too can be arrested only after an inquiry under the law. The judgment had also relaxed a provision that disallowed anticipatory bail.
Earlier this month, the centre had filed a review petition, saying the verdict had created disharmony, confusion and a lot of anger in the society.
The order issued by the Rajasthan home department last month, asking the police to implement the Supreme Court was taken back on Tuesday. Chief Minister Vasundhara Raje said it had been issued without her knowledge.
"I have directed the home minister and the police department to issue an immediate clarification on that circular. I want to assure the scheduled castes and scheduled tribes that we are committed to protecting their rights," said Ms Raje.
The Chhattisgarh government has put on hold an order issued by the police headquarters to implement the top court's order.
"We have always been sympathetic to the cause of scheduled castes and scheduled tribes. We will strongly put forth our arguments in Supreme Court," said Chief Minister Raman Singh.
After the Supreme Court delivered the order on March 20, many Dalit lawmakers from the BJP and its allies had conveyed their displeasure to Prime Minister Narendra Modi, demanding that the centre challenge the order.
Responding to attacks from the opposition, PM Modi had already made it clear that his government would not allow any dilution of the law.
The Supreme Court has already clarified that it has not diluted the law but had introduced safeguards to protect the innocents.