Congress communications incharge Randeep Surjewala asked Modi and Shah why they had not condemned the incident, and urged them to take action against a TDP MP who had allegedly threatened the writer.
Ilaiah had on September 23 filed a police complaint in Parkal in Warangal, Telangana, alleging that four people attacked his vehicle in the town and tried to kill him.
He said in a statement that "an atmosphere of hate and intolerance" was being created to "stifle the voice of those holding divergent views".
The Congress leader said the killing of journalist Gauri Lankesh and of rationalists Narendra Dabholkar, Govind Pansare and M M Kalburgi were a "definite pattern" and alleged that "lumpen elements having proximity to the ruling government take the law in their own hands and physically assault those who do not agree with a certain ideology".
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"The series of killings of rationalists, free thinkers and journalists has created an atmosphere that dissent, differences and divergence of views can endanger one's life. This disturbing trend cannot be and should not be tolerated," he said.
The Congress demands that the TRS Government in Telangana register an FIR and order an enquiry into the attack and intimidation of Ilaiah, he said, and urged TDP chief and Andhra CM N Chandrababu Naidu to take action against the MP.
"The BJP, which flaunts a mask of being the messiah of dalits and backwards, is maintaining a conspiratorial silence on the entire issue," he said, and asked Modi and Shah to condemn the incident and direct action against the MP.