Congress communications in-charge Randeep Surjewala said it was "unfortunate" that Prasad sought to link the slain journalist to the outlawed Naxals.
"Barely 72 hours after the murder of journalist Gauri Lankesh, the law minister has embarrassed the entire country with his controversial remarks linking the investigative journalist to Naxals.
"It is the country's misfortune that the BJP and the law minister are seeing a murder through political and communal colours," he told reporters.
A breakthrough eluded investigators three days after the journalist's murder outside her residence in Bengaluru. The Congress governs the state.
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Surjewala said, "There is a conspiracy to suppress the voice of the writers, journalists and activists."
In the three years of the BJP government, 10 journalists have been killed and 142 attacked across the country, he said, without giving further details.
He said that the BJP government at the Centre either disclose any evidence it has on Gauri's alleged links with Naxals or stop spreading misinformation.
When asked about the delay in the investigation into the 2015 killing of scholar M M Kalburgi in Karnataka, the Congress leader sought to deflect the question, and raised question about the delay in probe into the murder of Govind Pansare and Narendra Dabholkar in Maharashtra, ruled by the BJP.
Many people have drawn parallels between the gunning down of Gauri and rationalists Dabholkar and Kalburgi.
Surjewala said the killing of Lankesh was "celebrated" on the social media by several people who are followed by the prime minister on Twitter. He said this was sought to be justified by the BJP's social media chief, who described it as a part of the freedom of expression of these people.
The Congress leader also criticised Karnataka BJP MLA D N Jeevaraj for his statement that Gauri would have been alive if she hadn't written against RSS and BJP.
"Indrajit Lankesh is on record having said publicly that his sister was working actively to ensure the surrender of Naxalites...So was she doing it with consent and approval of the state government...And if so why was she not provided adequate security?" Prasad asked at a press conference in New Delhi.
It had also been said that Naxalites were unhappy with this. "Why was there such a security failure by the Congress government in Karnataka?" he added.