The law, introduced through an ordinance or executive order last month, stops courts from taking up complaints against ministers, lawmakers and officials without the government's approval.
It also makes it a crime for the media to report on any accused public official without sanction; journalists can face two years in jail for any violation. This is the part that is being reconsidered by the state government, say sources. Many have described it as a gag order against the media.
Amid protests and two petitions in court, the Raje government had yesterday tabled the ordinance in the state assembly. The BJP, with a comfortable majority in the house, had planned to enact the law after debate in the three-day session.
After Ms Raje's rethink, the bill maybe referred to a select committee instead.
The proposed law has drawn searing criticism not just from activists and the opposition Congress but also from at least two lawmakers of the ruling BJP, who have gone public with their disapproval. One of them, Ghanshyam Tiwari, even compared it to the Emergency of 1975 under Congress rule, when opposition leaders were jailed and the media was gagged.
The ordinance has also been challenged in the High court, with a petition arguing that it allows a "large section of the society the license to commit crime".
The Congress-led government of Manmohan Singh had first moved similar changes in 2013 to the anti-corruption law, apparently to protect honest officials. The BJP government in Maharashtra has already passed a law like this, but no law has tried to gag the media before.
The Rajasthan government had said a law was necessary to end "frivolous allegations" meant to defame ministers and officials.
Get the latest election news, live updates and election schedule for Lok Sabha Elections 2019 on ndtv.com/elections. Like us on Facebook or follow us on Twitter and Instagram for updates from each of the 543 parliamentary seats for the 2019 Indian general elections.