Nadda had last week struck a hardline tone amid protests in different parts of the country, saying the CAA will be implemented across the country and so will the NRC.
Shah had told election rallies during the Jharkhand election that the NRC will be done before the next Lok Sabha poll in 2024.
Some party leaders have conceded that the extent of protests against the CAA has taken them by surprise and pointed out that apprehensions in a section of society, especially among Muslims, over NRC have played a key role in whipping up emotions.
The prime minister, they added, has sought to defuse the situation by decoupling NRC with CAA and asserting that his government has not considered such a measure so far.
This assertion came as protests, some of them violent, rocked several parts of the country. Among the severely hit states was Uttar Pradesh, where 17 people died. A number of policemen have also been injured in clashes with agitators.
Asked about the fate of NRC in such a situation, a BJP leader said the message is "clear", after Modi's statement at the rally, indicating that party leaders are unlikely to rake up the issue in near future.
The BJP manifesto, it may be noted, has promised NRC in the country in a phased manner to combat infiltration.
Though Modi distanced the government from NRC, he also flagged the issue of infiltration in the country during his speech at the Delhi rally.
Infiltrators never "reveal" themselves, unlike refugees who never "hide" their identities, he said, accusing the opposition of not distinguishing between the former and those arrived in India due to religious persecution in neighbouring countries.
NRC is a key plank of BJP in states like West Bengal, where assembly election is due in 2021.
Another party leader said the BJP is free to promise it in states like West Bengal while going easy on its nationwide execution to cool tempers.
However, a decision will be firmed up in the coming days and weeks, he added.
Critics of CAA and NRC have said that their provisions are discriminatory and may be used to to target Muslims, a charge rejected by the BJP.
Modi had accused the opposition of stoking violence over the amended citizenship law and asserted that the legislation and NRC have nothing to do with Indian Muslims, as he sought to assuage their concerns.
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