"CPI is surprised at Modi's silence on such irrational and intolerant killing of innocent people. The party demands immediate action to bridle such anti-human forces," party general secretary S Sudhakar Reddy said.
The former MP also alleged that statements by BJP leaders justifying the "heinous" crime and blaming the victim and his family prove their roles in rousing "wrong sentiments" using the issue of cow slaughter.
He further charged that the Akhilesh Yadav government in Uttar Pradesh had delayed the police action in the case and alleged that widespread moves were being made to bring about communal polarisation.
"This is the height of intolerance that just on rumours and suspicion, Mohd Iqlakh was killed. Nowhere in the world are people being killed for eating non-vegetarian food.
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"CPI once again reiterates that eating habits are an individual's choice and none should dictate what to eat and what not to eat. It is gross interference in personal freedom and violation of basic human rights," he said.
Speaking to reporters in Delhi, Sharma had said, "This (incident) should be considered an accident without giving any communal colour to it." He had added that he feels the "incident occurred due to some misunderstanding".