The Aam Aadmi Party (AAP) also went to the poll panel, seeking action against the former Gujarat minister for spreading communal hatred.
"The EC should not allow such elements to create hatred at such a sensitive juncture, when the country is in the midst of a general election. The remarks openly incite people of one community to take revenge against another religious community and cannot be allowed to go unpunished.
"It should immediately order registration of a criminal case against the BJP's national general secretary Amit Shah for his inflammatory remarks aimed at spreading communal hatred," the AAP said in a statement.
A complaint to the poll panel and minorities commission was also filed by Delhi-based lawyer and activist Shehzad Poonawalla.
BJP spokesperson Nirmala Sitharaman, however, said: "We see nothing wrong in Amit Shah's statement."