While Chhattisgarh, Madhya Pradesh and Rajasthan had reportedly taken steps to implement the order, they have now decided to put its execution in abeyance and approach the top court for a review.
"We have spoken to these chief ministers and their governments will soon file a review petition in the court. It is natural that the implementation of the order will be put in abeyance till the judiciary takes a final call," the party leader said on the condition of anonymity.
The court recently laid down guidelines to prevent the alleged misuse of the Scheduled Castes and the Schedule Tribes (Prevention of Atrocities) Act.
Dalit groups have, however, vehemently protested against the verdict, saying it dilutes the law and will lead to a rise in cases of atrocities against the scheduled castes and tribes.
The Centre has already filed a plea seeking review of the Supreme Court directive in the wake of largescale protests by Dalit organisations.
In its order on March 20, the top court had said the law's misuse had led innocent citizens being framed as accused and public servants deterred from performing their duties, which was never the intention when the Scheduled Castes and the Scheduled Tribes (Prevention of Atrocities) Act was originally enacted.
As per reports, Chhattisgarh, Madhya Pradesh and Rajasthan governments recently issued formal orders, instructing their police chiefs to implement the March 20 Supreme Court order.
After the judgement, various Dalit MPs from the BJP-led ruling NDA alliance, including Ram Vilas Paswan and Ramdas Athawale, had met PM Modi to expresses their concerns and demanded that the Centre should challenge the order.
PM Modi has also asserted that his government will not allow any dilution of the law to prevent atrocities against SCs and STs.