(Read the full interview here)
The Bharatiya Janata Party (BJP), put on the backfoot by the comments, insisted the remarks had been "misinterpreted" with an aim of "appeasing a particular community".
The Congress demanded Modi apologise to the nation as his words are "totally against the idea of India."
"Thousands of people were killed in the communal riots in Gujarat in 2002 and in the backdrop the analogy used by Narendra Modi needed to be strongly condemned. There is no place for such a comparison in civilised India," party general secretary Ajay Maken told reporters.
Samajwadi Party spokesman Kamal Farooqui took strong exception to Modi's comment that even "if a puppy comes under the wheel" of a car, he would be sad.
"It is a very sad, very humiliating and very disturbing statement... What does he (Modi) think, that Muslims are worse than even puppies? He does not have a heart for them. He should feel sorry... He should apologise," Farooqui said.
BJP spokesperson Nirmala Sitharaman sought to defend Modi, saying his comments had been "misinterpreted" completely, resulting in a "controversy where it does not exist".
Describing the controversy as "absolutely despicable", she said, "I appeal to all to read the interview in full and not to speak out of context. It is risky. On the 'puppy' comment, she said Modi meant that anybody would feel sad even if a human being comes under a car.
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