Haryana BJP's chief media coordinator Suraj Pal Amu has reportedly put a bounty on their head and also threatened actor Ranveer Singh, who also stars in the movie.
In its letter to the Haryana DGP, the NCW asked him to "look into the matter immediately".
The NCW, in a statement, said it has taken suo motu cognisance of media reports on Amu's remarks.
Amu was quoted as saying, "I want to congratulate the Meerut youth who announced a Rs 5 crore bounty for beheading Deepika Padukone and Sanjay Leela Bhansali."
"We will reward those who behead them with Rs 10 crore and also take care of their family's needs," he said.
After widespread protests, including threats, the makers of the film have deferred its release from its December 1 release.